I'd also second Shadowrun 20th Anniversary Edition (AKA SR4A). It is a refinement and reorganising of SR4 (and looks a thousand times better), and both "editions" use the same books.
I think SR4A feels the most accessible. It's less chaotic on the page, brighter and cleaner design-wise, has better and clearer writing, has much stronger editing, and is generally not quite as full of side cases and exceptions as SR5 (or SR3).
I prefer point-buy to priority chargen, but both options are available in SR4 if you get the Runner's Companion. The default priority chargen of SR123/56 has trap builds in it, which I despise on principle, as it means some players start the game worse off just because they don't know how to play the chargen minigame.
I also find the optional rule to use a target number of 4+ rather than 5+ means you can let players diversify their character sheets more. They don't need to stack dice pools quite as high, as a dice pool of 10 will reasonably handle even "extreme" difficulties. Most characters will only need 8 dice in their core areas of competence. Priority chargen exacerbates that issue, IMO.
The Matrix in SR4/SR4A gets slated, but I'm not sure SR5 is any better. The core of SR5's Matrix rules is slightly easier to grok, but they've layered so much faff on top that it's actually much harder to track in practice. All of the extra "noise" (that's a pun, but you'll see why later) interferes with comprehension and the at-the-table experience.
SR4A is the opposite -- you feel like you can stick with the simple stuff and only need to add in the complexity if you want it.
First you use Matrix Perception to see if you can find/detect things in the Matrix (if they're hidden/non-obvious), then you acquire user access (user, admin or security level), then you do what you want to do. It roughly works out the same as breaking and entering for mundanes: observe, infiltrate, then attack/steal/whatever.
(If you really need an entire SR4A Matrix rewrite, Google "Ends of the Matrix Frank Trollman", and you'll find something that works but is long-winded.)
Note that SR4/SR4A also has some nice "Tweaking the Rules" sidebars that give you some neat options (SR5 and SR6 does this to a lesser extent, too). Those help a lot with cutting back on the crunch. E.g., you can ditch Damage Resistance (soak) rolls, and make it a static damage reduction instead (I'd make it DR/3).
More recently, there's Shadowrun Sixth World (SR6 or SR6W, I guess), which looks a lot simpler at first, but suffers from the editing issues of SR5 dialled up to 11. Design-wise, it looks great on the inside, although the covers don't really do it for me like SR4A or SR5's did.
There are also currently two different SR6 core rulebooks out. There's the first printing with errors, and then the Seattle Edition (third printing, I think) which has some errata and a section on Seattle.
There is a third CRB one on its way (the Berlin Edition), which aims to add setting info on Berlin. Although, if you get the PDF, I think you get access to all three versions.
SR6 is definitely interesting, but I feel like it needs an SR6.5/35th Anniversary Edition to be smooth rather than merely functional. It's easy to get into, though -- most of the problems emerge in play, rather than being obvious upfront.
Shadowrun Anarchy is my current favourite as a GM, but that also suffers from poor editing. On the plus side, the system is simple enough that even a newbie won't be intimidated, and that makes it relatively easy to cobble together any holes or gaps in the rules.
The biggest issue, for me, is that the core rulebook assumes familiarity with the world (though you've got several wikis to draw upon).
The Anarchy CRB also suggests a narrative style of play most people won't use by default, but that can also be ignored with minimal effort.
We're playing Anarchy and it's both fast and incredibly fun. If I were to go back to SR5 or SR4A, I think I would port in the unified karma/nuyen rewards of Anarchy, plus the rebalanced "amp" system, and use those to replace the entirety of the fiddly gear/cyber/resources part of the game.
In the meantime, I will probably introduce a couple of house rules, but it doesn't need much and it's easy enough to port things in from the other editions. surprisethreats.com offers lots of new advanced and fixed rules for free.
SR4A especially feels good and complete, and has all the gear porn, kooky metatypes and so on that draws people to Shadowrun in the first place. Many people will point out that it's also the last edition to have many of the "older" Shadowrunner writers on it, as most (all?) of them left in the latter half of that edition's cycle.