Personally I would look at a decent 720P DLP projector. Should be able to get one well within your budget. I own an Optoma H78-DC3 and I'm quite happy with it. Since you are talking about a permanent screen (screen goo) I would buy a fixed 1.0 gain screen. Adds a little more to the budget but there may be some savings from the projector.
As far as speaker cable, you really need to run no smaller than 14ga wire in the wall (12ga better). The cable needs to be rated UL CL2 or CL3 unless you plan on running conduit.
Most important:
Jaxvon is right. If you think you need 100 feet of wire, once you start running it in the wall you'll need 200 feet. It never fails, you think you can get four 25ft runs out of a 100ft spool. The roll ends up having 97ft on it and one of you runs ends up being 30ft
You can't splice cable, so the runs have to add up to what you can cut from the spool. I really doesn't cost that much more to buy bigger rolls. It was cheaper for me to buy a 500ft roll instead of a couple smaller 200ft rolls.
