If it's a game you're teaching yourself, 4th Edition is the best of the options you've chosen for yourself.
Now, the best edition of Shadowrun to start with is the one that's already being run by an enthusiastic GM you already get along with. Learning a game on your own can be difficult, since the actual thing you want to learn is how to play the game with others and, well, there's no teacher like experience.
But sometimes, it's the only option you have, and that sounds like the situation you're in. I'd actually favor 3rd edition over 4th, and 3rd is still available at PDF retailers like DrivethruRPG (not true of editions prior to 3rd as far as I know) even if the physical books themselves are only available secondhand for $yikes. The reason why is... hoo boy, this is going to take a while.
The short of it is that Shadowrun has always had problems, and the progression of Shadowrun between editions has mostly been a mixed bag that addressed some problems but introduced new ones. It may just be my bias as someone who's been involved with the game since the 1st edition, but for all that 4th edition improved and tried to improve, it also lost a lot of useful things, and later editions have committed to that direction.
Shadowrun has always had problems.
I don't think anybody will tell you that there's such a thing as a turnkey edition of Shadowrun, one that you can just believe will give you a good game if everybody plays in good faith. Every edition of Shadowrun requires some work and awareness outside of what the book tells you.
Shadowrun is tough to make characters in. Every edition has some kind of point-buy character creation system, where you're given one or more pools of points to spread around your various capabilities to make a starting character. But when you have an idea for a starting character, how do you turn that into a reasonable distribution of points? What skills should you have, and how high? How do you spread your attributes to support them? What gear do you need?
You could stack everything on one single skill if you wanted, but by necessity every shadowrunner's got to be a bit of a generalist. You're out there doing crimes to not starve and you can't exactly stop halfway through a crime to ask a security guard to hang on while your buddy who's good at talking to people crosses the corporate complex. In the pressure of the moment you might have to drive somewhere, get information out of someone, survive a fight even if you can't win it.
It's legitimate for a majorly specialized somebody to exist in a cyberpunk story, but that somebody is almost always a former corporate operative who finds themselves very disadvantaged when they're trying to do something the corporation "had people for". Where is the functional baseline, and how are you putting yourself under it to boost something else? This is a question no edition of Shadowrun has ever really had a good answer for. You might think that the pregenerated characters might be good starting places to work from, but the other thing about Shadowrun is that the pregenerated characters aren't necessarily intended to be at parity with each other -- and that's if their stat blocks are even valid for starting characters in the first place, since they may have been made on a different revision of the rules than the final one printed in the book.
Shadowrun is tough to make opposition in. Shadowrun is generally a pretty symmetric system, where players and any character opposition the GM would like to stand up are rolling from the same statblocks to get the same number. So take all your personal questions of balance and multiply that by every significant person the GM might want to prep. Even when the GM isn't preparing a full character - if they're trying to figure out how tough it is to pick a lock, hack a camera, or break down a door - there's still always the question of "based on what I know about how relatively tough this ought to be, what number do I put on it?" How do your structure your shadowruns to be challenging without stonewalling your PCs or accidentally making something lethal?
Shadowrun is tough to run. The rules of Shadowrun have historically been developed to favor the independent mechanization of independent variables - rather than collecting into a single number, important facts of the scenario that aren't necessarily linked have their own mechanical presence. So you're trying to hack a camera. How sophisticated is the hardware? How advanced is the software? How many resources does the hardware/software system have to work with? What security level does it assign to the operations the PC is trying to interfere with? At some point in the history of Shadowrun, the answer to each of these questions has informed a separate mechanical value in the rules, which each fed into the overall process of hacking.
But when you're trying to adjudicate a shadowrun, what that means is that every time the PCs do something different you may have to rotate over to a different set of rules, a different set of expectations and modifiers.
Shadowrun's fictional inspiration doesn't lead to stories where everyone's always involved. In contrast to what I said in the character section, cyberpunk fiction where multiple characters are involved is usually some kind of heist story, where each character does have some kind of specialty that will be needed for a heist and characters don't need to have an active presence in scenes where their specialty isn't important. A story can be exciting even when it spotlights one person at a time for long stretches, but the same isn't always the case for a multiplayer game.
Like, you know how it looks when you hack a camera in cyberpunk, right? You plug a glowing cable into a convenient wall socket, your consciousness enters the cyber dimension, you speedrun Elden Ring glitchless any%, and then three real-world seconds later you snap back to reality and the camera powers down. That story, which only involves you, maps by default onto a system that only involves you. It's always been a struggle for Shadowrun to create good specialties with clear strengths without also reserving a chunk of play time for their exclusive use.
The progression of Shadowrun has always had problems.
Every game has some bumps when moving from edition to edition, but some of the particulars of Shadowrun's design means some concerns are more likely to show themselves.
Shadowrun's design is complex, so the first version of any new system is often flawed. Mages who use magic to reinforce their own bodies rather than flinging spells around. Computer users who specialize not in bending hostile systems to their will, but in controlling friendly systems - drones and vehicles built to be remotely piloted. These and many other concepts show up in a first draft, maybe in some side material rather than a core sourcebook, and may have mechanical problems or an unclear role in the game when they first appear, and usually it takes until the next edition for their rules to be cleaned up and (partly or fully) bulletproofed.
Shadowrun's design is complex, and rule changes often arise to try and make it simpler. The overall trend of Shadowrun has been to reduce the total number of moving pieces in the resolution process; even as new systems are introduced, the overall resolution process tries to get simplified so the game can be run more consistently from activity from activity. This transition in particular will often get people's hackles up because Shadowrun's complex design is often there to reflect independent influences on whatever process the rules are trying to model. In moving to a simpler design, the rules also shed some fidelity of modeling, and people feel that loss.
Shadowrun is set sixty years in the future, and is thus always in continuity with itself. I don't mean that metaphorically, I mean that any book set in "the current year" of Shadowrun takes place at least 60 years after its publication date - it goes up and down a little based on what edition you're looking at, but it's at least that much. If anything changes in the setting, there's often an explanation for how that change actually occurred in the world fiction, even if the thing that changed was a game mechanic for game mechanic reasons and the world-fiction explanation has to get backfilled on top of it later. Every edition of Shadowrun contains the whole past of Shadowrun, with all its idiosyncracies and problems.
Shadowrun is set sixty years in the future, but the future has to advance along with the past. Surely you've seen science fiction stuff made in the 70s and 80s where humanity's cutting-edge space technology centuries into the future was still using cathode-ray tubes and VHS cassettes. Projecting the future development of technology has always been more guesswork than science, and when it could Shadowrun has tried to dodge around that, such as recalibrating computer processing and storage to work in made-up units. But that only gets you so far: in the years since the first edition, we've seen the rise of flat screens, wireless computing, "serverless" code (really it's all just running on someone else's computer but you don't care whose), social media, smart devices of varying smartness but always smaller size -- and we've also seen some technologies that were supposed to be the spearhead into the future, like virtual reality, run into roadblock after roadblock when they tried to actually get implemented. As a result, some mechanical development often gets devoted to realize "advances" in past technology that are getting too obvious for them not to endure into the future somehow, regardless of how well they actually work with existing mechanics.
The advancement of current technology is invalidating the cyberpunk fantasy. Maybe that's being too overbroad; cyberpunk appeals to a lot of people for a lot of reasons. But one of those fantasies is turning the corporate state's constructs of surveillance and oppression back on itself. As we see the spread of technologies that make surveillance more omnipresent and analytics give corporations a better and better window into everyone's lives, it feels less and less likely to actually be able to slip or subvert the net.
Let's talk between-edition changes.
So here's the starting point for Shadowrun, published initially by the FASA Corporation: a high-tech, largely urban, setting with geographic states but corporate power blocks. A digital world within the wires and an astral plane mages will occasionally visit. Magic rises into the world after a long period of dormancy. The previous rise of magic was the Fourth World, where the company's fantasy RPG Earthdawn takes place, ending in apocalypse; the human history you or I might know about took place in the magicless interregnum called the Fifth World; and Shadowrun itself takes place in the Sixth World.
Engaging the game mechanics where the outcome is in doubt means assembling a pool of exploding D6s and rolling them in pursuit of a variable target number, with the margin of success increasing your base result based on a variable step number. The initiative roll is extremely open-ended with many sources of bonuses - you go on your initiative count, then subtract 10 and if that's still positive that's the next time you'll go.
What follows is not intended to be a complete list of changes, because these are 300-page full-tall books we're talking about, but just a summary of some of the advancements and sticking points.
1st edition to 2nd. The "variable step number" mostly drops out. Most of the variance was between different weapons, and this takes out some points of distinction between one weapon and another. Physically-reinforcing mages, "physical adepts", get a better fleshed-out rule treatment in the main book rather than being side material.
2nd edition to 3rd. Device-controlling hackers, "riggers", get a better rule treatment in the main book. The value of a high initiative is notably de-emphasized - you'll still get multiple actions in every combat round, but everybody goes once before the people with enough initiative to get more actions go again. You get a small dice pool for bonuses to your attacks and defenses in combat, and while it had refreshed every initiative pass, as of 3rd edition it refreshes every combat round instead. But especially in its splatbooks, 3rd edition introduces rule systems to handle things GMs might have previously handled ad hoc, like crossing national borders or surviving in harsh conditions.
3rd edition to 4th. A big transition, as the RPG moves from FASA Corp ownership to Wizkids, who licenses the production to Fantasy Productions, the company responsible for providing the German-language version of Shadowrun. (This is no small achievement; Shadowrun is pretty big in Germany and the German-language version has some sidebooks for running in and around future-Berlin.) The parallel worlds collapse; mages and deckers now interact with overlays on the physical world. In the decker case this is due to a collision between escaped experimental AI and the most important high-frequency trading exploit in history, causing the wired Matrix to become permanently compromised and sending it completely wireless.
Variable target numbers for dice are now gone, with every die always having to roll a 5 or better to succeed. The sometimes-confusing system where your pool of improvement points and globally-available rerolls were both named "karma" (well, "karma" was your improvement points and "karma pool" was the rerolls) is replaced with a system where "Edge" is your reroll stat and can be developed independently of your total karma count; it also subsumes most of the previous per-activity dice pools. While it had been a side-option before, character creation moves away from category priorities, which set your points budget for each, to an overall global point budget.
4th edition to 5th. Wizkids is bought by Topps, and the Shadowrun license passes to Catalyst Game Labs. Catalyst... can't pay for good writing and editing. Not that you can look at the book credits to see bad writers and editors to avoid, but rather, even if they did hire good people, they didn't pay them enough to spend the time they'd need to spend to do good work. 5th edition is shot through with inconsistencies, missing references, rules updated in one place but not another, and game mechanics that do nothing. The Edge system, admittedly slightly overtuned in 4th edition, is scaled back a bit, and the concepts of "limits" is introduced, capping the total number of successes you can achieve in a scenario based on some scenario parameter, no matter how many dice hit the table.
5th edition to 6th. The game tries to consolidate its rules even further, after the pattern of the rules-light alternative system Shadowrun: Anarchy, consolidating a lot of scenarios and modifiers into a system of situational Edge and rerolls. But Catalyst is still responsible for the book production, and problems continue. Draft and placeholder text show up in the final product. Some character attributes become effectively useless. The net effect of wearing even the most sophisticated armor is denying the attacker one or two rerolls, which is not even expected to be one success.
Why do I prefer 3rd over 4th?
I should start off just to say that as someone learning the system for the first time you're probably fine with either. I would not recommend learning the game from a Catalyst Game Labs edition because you'd wind up encountering rules that were just wrong. Both 3rd and 4th are available electronically for reasonable prices. And part of it is just because I was there for the change, having come up from the origin of the game. There's an unavoidable bias toward the things you learn first.
The fairly large plot revision in 4th moves the game away from the foundational works of cyberpunk and more toward contemporary high-tech heist and crime fiction. This may not even be a downside for you at all, depending on what you're a fan of. (And honestly, the game has never really been that faithful to the foundational works of cyberpunk.) It does move away from the extended-spotlight problem I mentioned above, but what it introduces is the idea of an external wireless threat. The idea of someone coming in from outside to compromise your personal electronics means something more in a setting where "personal electronics" include the things that let you stand and breathe. Tempting outgoing, terrifying incoming.
The move to static target numbers in 4th edition simplified overall resolution but drastically reduced the power of second-order effects. And honestly this may also be a point in its favor for you. The only things to worry about when adjudicating a test are how many dice to roll and how many successes you need. And for reducing workload on everyone during the game that's just fine! But because any given die only has a 1 in 3 chance of success, any game mechanics that effectively "roll dice twice" are more or less meaningless unless you're rolling double-digit numbers of dice to begin with. Like: if you're trying to cram for a mission by reading bomb defusal manuals or whatever, roll Logic+Knowledge and take that number of successes as bonus dice on your roll to remember the schematics later. If both of those stats are high you might get one more success, maybe two. It's really just something to keep an eye out for, which as I've said doesn't mean a whole lot since you're always keeping an eye out for something.
Whatever you choose, good luck.