I just have some half-assed observations with no sources and no specifics.(typing on phone)
You won't be able to just project on the wall. Even if the wall is white, it might still come out dim. You need something more reflective. That's why those pull-down projector screens exist. If you ever shine a laser at one, you'll see that they're made of some kind of micro-reflective stuff.
You don't have to buy one though; there is also such thing as special paint just for projectors.
As far as what you want to do with it, it'll probably have a HDMI port for laptops and USB inputs and red/white/yellow jacks and even that other one that's red/yellow/blue/green/orange that started around the time PS2 came out. Nowadays they have wireless capability, too.
In short: you'll be fine. Just check Consumer's Reports for a projector review, or something. All in all, it's not a bad idea.
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