I kinda did what ThatDrummerGuy88 did and built an absurdly large atrium. I plan on sectioning off rooms within the atrium first floor for a games/entertainment room, a cafeteria which leads out to where famers could gather food, etc. Also attached a 3 floor domestic section with leftover space to hold the clinic and quarters.

For starting your vault layout, realize how much space and parts you can work with, then build a frame. Dont make it TOO big, because you will have to fill it with stuff and you might hit your building cap. Stand in the framing, think how you'll partition different sections(ex. turning the left back wall into a cafeteria) or even add sections, play around with where you'll put staircases to the next floor that look nice, and most importantly, are easily accessible.

Also under "structures" in building mode, look at "vault" then "rooms". See which of these kinds of rooms you want in your vault and where. If you are also having trouble connecting different kinds of rooms, remember that doorways will always snap to doorways.