Alex, you have a great many options from which to choose.
First off though, you will need to run component, especially if you want to take advantage of progressive scan, which you won't get via the s-video. I would personally recommend a mini bnc cable. Basically, it is five composite cables (R, G, B, H, & V) with a jacket around them. This makes it easier to install through the walls or conduit. The ends are ternminated with bnc connectors. This is especially made for HDef but you can use just 3 of the cables for component and have 2 cables as spare when needed. Provide us with the dynamics of the room for possible wiring solutions.
As for the projector & screen, once you have nailed down a projector, then you can decide on the matching screen. You basically have crt, lcd, dlp options available to you at that price. Take a read through this on the basics...
Front Projection - How do I select one for my needs? for starters.
I know of a few very nice digital projectors and screens that would fit that $5K budget nicely.