As a first time DM I found a group to play Storm King's Thunder. I have been reading the first part of the story to prepare. So far I have read up to level 5 till after the flying with the giant to one of the 3 towns, but I am worried that I might miss parts of the story that are important for the players. Like bits of lore or things that the PC's might ask that I do not know.
Should I read further ahead or should this be enough for a while?
For me, I would advise fully reading all the information provided for a given campaign.
Given that all PCs in the history of tabletop games either accidentally or deliberately subvert DM expectations and plans, a fuller understanding of how the story will play out will help you 'correctly' seat your improvisations within the overall canon.
Most importantly this can help you to avoid retreading themes and scenarios that might occur later. (A fight with a new major NPC vampire is a lot more impactful if you haven't just encountered one in the abandoned house that you mentioned on a whim that the players refused to ignore).
Doesn't need to be complete, but you need to be aware of the events that occur, the characters who appear and the places it is feasible to visit at a minimum.
You don't need to remember all the details, just the overarching themes, major characters and plot points.
bits of lore or things that the PC's might ask that I do not know.
Players will always ask questions that you haven't prepared an answer to. When they do, you make something up. By reading ahead, you aren't trying to build an encyclopedic knowledge of everything. It's impossible; even the adventure writers failed to predict all of your players' questions. You're trying to internalize the story-critical information, so that you can make stuff up without setting yourself up for a big contradiction later.
Reading ahead also let's you add in your own foreshadowing of later story developments, or to recognize the foreshadowing that's already written into the adventure so that you can emphasize it properly.
Prepare in depth for only one play session at a time. This allows you to incorporate events of the previous session or emphasize longer-term consequences of player decisions. This is how you make a campaign feel organic, while still sticking closely to the script of the pre-written adventure. This also allows you to focus your creative energy on one session at a time to make it as great as it can be.
Often you will find that your group will take two or even three sessions to complete your "one session" of prep. That's fine, just refresh yourself on the material before each subsequent session, and make modifications as necessary to adapt to the events of the previous sessions.
Much more rarely, the group might blow through your prepared materials, completing it all with time to spare. In this case, you can either improvise, or end the session early and find some other way to enjoy the rest of the time with your group.
Assuming they are starting as level 1 characters, prepping for the very first session should involve close scrutiny of the Tier 1 information (Levels 1 - 4). While there's no harm in reading ahead as an FYI, you want to be clear on the material that is likely to involve them in their immediate next session.
They should not encounter any of the detail of the Tier 2 material beyond lore and story as you mentioned; it's good to read through it all and see how the story plays out, but the gameplay itself will suffer if you mix in too much encounter material from later tiers.
As a new DM you will be astonished at how little progress your players make through an adventure in any one 3 hour session; They may only get into a single area and end up staying there all night. 4 encounters is normal, 6 feels like a lot; sometimes there may be none, when characters are restig in a tavern, restocking/resupplying or just carefully investigating non-combat areas.
The advantage of the prewritten modules, and especially linear dungeon areas, is that you can usually determine what the next 4-5 encounters are most likely to be, and ensure you're prepped for those (mainly, familiarizing yourself with monster capabilities, their best attacks/combos, their escape routes, and their motivations) as well as traps, items of interest, and loot/treasure info. If you are using wandering monster encounters, prep the same for those - basic monster stats, capabilities, motivation - why are they wandering, after all?- plus escape routes, and treasure, if any.
When creating and prepping your own material, this is still a good rule of thumb - identify and prep the next 4-5 most likely encounters and you'll be in good shape. The advantage with homebrew is you are always off script, so you're more free to come up with your own filler when characters immediately start breaking through a wall and into an area of the dungeon they weren't supposed to get to for six more weeks.
The downside with homebrew is that you abandon a lot of material, but you can be more effective there too by only prepping for 4-5 encounters per session so you don't feel so bad about losing weeks/months of prep on an elaborate plot that they are now totally uninvolved in, in favor of some other thing you threw in on a whim in session 1 (that's me right now, in Session 17, where the players diverged in the very first episode based on my idea of having them find a baby instead of treasure in a basket).
I am a new DM as well, having run SKT during a week with friends in a flat just a week ago. My players loved it. Here's how I did it, and what I would do differently:
I read some of these summarizing articles, but especially this guide first. It's quite quick to read and gives you an overview over the whole plot.
I then started reading the campaign book, and pasted all the stat blocks from the monster manual together on some paper so that I wouldn't have to look for the stats during the game. That was very useful.
I printed some generic Maps and scans of the maps in SKT. That was not very useful (yet), but the map for Nightstone is great to have on the table, for the players to see.
They didn't notice the rocks lying around on the map for quite long, and were very surprised when I told them what they see :D
I also printed the spoiler-free map linked in the first comment here for the players to see, to give the players the feeling that this is a world where they can go to wherever they want.
They are now still in Nightstone after playing on several days. (I find it hard to estimate, but at least 20 hours playtime for sure! Without character creation.).
I haven't even run the earseeker event yet, and they have not visited the dripping caves.
However, since I expected them to do the unexpected, I have read about all the locations that are detailed in chapter 3. I feel like I prepared wayy too much, but it makes it now a breeze to prepare the next session - I can skim over the nearby things and am ready. I would recommend to read until the end of chapter 3 if you really have the time for that.
Sure, reading the whole campaign would be better, but I doubt the difference is worth the risk of never playing that far that it becomes really relevant.
Make sure you have at least something generic ready that would make sense if the players digress completely from what you expected, but my players did pretty much what I expected, even though I was prepared for them to go litterally anywhere else on the map.
Since I had quite some time for preparing, I also googled a lot about SKT. The main complaint I have found was that people consider it to be not fleshed out enough in the travelling sections. But that means you can come up with PC-specific plots and mesh that with what has been prepared. In my short experience, preparing for only the things that are nearby is enough, as long as you have a general sense of the over-all plot, so that you can insert some foreshadowing or relevant details as needed.
