I'll make a few things simple for you, you can thank me later...
The design of the room - you need to determine the seating distance, and how much light comes in on Sundays (for football) - then you go shopping for a projector. Epson's are good for dark to low room light, Panasonics for higher lit rooms. Don't bother with the high-end Sony's, JVC's unless you deem yourself a movie freak and need ultra-accurate color. Cost of decent projector is +- 2000. The newer laser projectors are great for up to 100" and are about 1500 more. If you are on a budget, don't even bother with a screen, new well sanded gyproc painted flat white will be just fine - I'd put that money into my speakers instead. If it ever bothers you that "the blacks are not black enough" then save and buy a screen.
Get your cables from monoprice.
For your audio system, the highest cost will go to your speakers. That is personal and budget taste. Most brand receivers are good. I personally like the Marantz, and Yamaha's for sound.
As for the room itself - plan well. Isolate inside the walls but don't go bananas - unless you plan on going the whole way. By this I mean if you want a completely isolated room, you can do so, but it takes serious planning and execution - unless the room is completely sealed, air leaks means sound leaks. This includes the way you hang your gyproc, the caulking you use for corners, double hanging gyproc, doors with seals etc. I personally wouldn't bother. Insulate, get solid core doors, be happy. When the room is finished treat it. There are a few local guys that build 2x4 sound panels for studios using proper solid rigid insulation - they are about 60 a piece. If on a budget make sure at least your corners are done (about 120 a piece), first reflection points (look it up it is easy to know where those are), and your back walls.
I suggest you get recessed led's. They throw no heat, are easy on the eyes, and dim nicely. I would buy Casetta light switches.
Install a sink, buy a fridge and a microwave. Get a comfy couch. Enjoy.
It is all in the planning, do not let a contractor make the decisions for you.