I'm a first time DM creating a game for some buddies. None of us have ever played (myself and one other player watch Critical Roll), and I want to set the campaign in the geography of Westeros. Outside of the setting, I don't really have a specific story in mind, I'm currently planning on letting it come to me as we work thru our first couple of encounters. My main question is: Is there a certain canon or umbrella story/background that most of the published D&D adventures fall under? I'm looking for a general knowledge base that it can be assumed any character within the world would know.

It's a generic answer but; your characters/players know what you tell them, that's it.

Of course everyone who plays comes in with preconceived notions based on their understanding of pop culture, myths, lore, movies, books, etc. This type of meta will influence how they play and what they'll expect. From there you start to refine these expectations and give them the framework of how the world actually works. 

When you start a game you begin with session 0, where you set up the framework. You'll introduce the setting, special rules, table etiquette, all the basic information you and your players need to know. This information is based on the module you are running, the setting you've chosen to play with, or the homebrew you've whipped up.

As to an over arching theme, that tends to change based on the setting. You have Forgotten Realms, Faerun, Greyhawk, Ravenloft, Underdark, Ebberon, and so many offshoots. Each one has different cannon, lore, political situations, pantheons, so on. However, the common theme is that your players are heroes, there is a threat to overcome, and the journey from zero to hero.

I know it's not much, but I hope it gives you food for thought. Cheers, and welcome to this side of the screen, many happy games!

Of the adventures published thus far by Wizards for 5e, most of these occur in the Forgotten Realms setting. You can probably google it. I'm sure someone's written a wiki on it or something.

Thing is, that's a whole of lot history and background which isn't necessarily going to come up, be cared about, or even be necessary, simply because there's too much. To tell you the truth, the PHB and each of the adventures probably contain enough. I would hazard that most people coming in to Dnd reasonably survive with no working knowledge of the Forgotten Realms apart from what they learn as an adventure unfolds.

I'm not aware of there being anything out there for westeros at all, I'm a firm believer in treating players like mushrooms anyway so in general no

Start them naked in a ritual circle with no memory of how they got there and no knowledge of the world they live in...

Maybe they are shmucks who got rolled after a dice game, but who knows, maybe they end up being fallen gods rediscovering their divinity or individuals whose consciousness has been transferred from our world (a la The Sleeping Dragon). In the latter case, it might even be funny to use a different, but similar, game system’s set of rules to confuse them.

or just let them discover their classes. Different rules is a bit much if you are new to this. 

Quote from Greg >>

Start them naked in a ritual circle with no memory of how they got there and no knowledge of the world they live in... 

I've thought of doing this myself, after watching the pilot episode of Dark Matter. I think this could be an interesting way to set up a campaign, especially if you found/created mechanics for them to remember and discover their abilities and skills ( really just an in-game method of rolling up characters ).

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There are actually several canonical histories and stories - but these are tied to specific settings. Forgotten Realms is the most obvious and probably most developed, but each setting has its own ( Eberron, Greyhawk, etc. ).

So far as I know, there is no published material for Westeros.

DMThac0's suggestion that you all sit down and work out game exceptions through a Session 0 is a good one. Here's a sketch of what I try and put in a Session zero here.

Given the fact that you're all new to the game, I'd suggest you to try something a little more modest for now - like a published module, in a generic setting, with pre-rolled characters that your Players may-or-may-not keep. 

Sort of a set of "training games" for you and your players before you decide to buckle down and play a consistent session-over-session carryover.

You may find it easier to get used to the game, and work out your mistakes ( both as Players and as DM ) before you're forced to live with them long term.

But - welcome to D&D! - and best of luck, no matter which path you decide to try with your campaign :)

A lot of DMs who want to use their own stories make the mistake of starting with really broad things about the setting, like the legends and lore of the realm, the geography of the world, the pantheon of gods and goddesses, etc., which is fun to come up with, but usually has very little bearing on actual gameplay. It's much better to start with the local area the PCs begin in, and work your way out from there. How did the PCs meet? Why are they working together? That's something you might want to give them input on. I'd start by coming up with a relatively simple quest to give your players, something that can be resolved in only a few hours of play. Maybe come up with a base the PCs can use, like a town (what services are available in the town? What's the blacksmith there like? Those are things you'll probably need to be prepared to deal with, not questions about the history of the town or its culture). Then give them a destination to travel to and a reason for traveling there. Then come up with some ideas for stuff that might happen, or people or creatures who they might meet, on the way there. That's more how you write modules for D&D. I'd start with a fairly linear story if I were you- those are much easier to run than branching story lines, or at least they take much less time to plan. Leave the players with choices, but don't give them reasons to make choices other than the ones you intend for them. 

Find or create a map of the whole land, but really simplified. Don't worry too much about all the small towns, and traveling roads, you can create those through the gameplay. Create one town, city, or open field, or mine labyrinth for your players to start out. Make this first location a session or two long so you have time to set up joining locations, and figure out how you want to DM the campaign. Where you start out can have your players decided how they will start playing their character (do they like to watch what happens, steal everything, murdering hobos, etc..) Once you have a grasp on what motivates your players, and they understand their role in the party start moving them to other locations. If they want to leave sooner, tell them you aren't prepared to have them leave quite yet.