A good starting place is Projector Central
. You will be able to research all the best projectors in your price range. You should be able to find an awesome projector for $2000 or even less. When I bought my projector three years ago, the two big names in that range were Panasonic and Sanyo. They were always going head-to-head, making for some interesting comparison reviews. Seemed like Panasonic came out with a new model every six months. I haven't checked the product lines out in detail lately, but I'd start by looking at the latest offerings from those two companies.
When you get ready to purchase, there are many sites that have good deals. I bought a Panasonic AE900 from Visual Apex
and was very happy. Here's
a link to the Panasonic PT-AE4000U, my projector's great-great-great-grandchild, which lists for $2499 and is $1999 at Visual Apex. I'm sure you could comparison shop for a lower price on the web, but, of course, make sure you're buying from an authorized, reputable seller.
I use a Da-Lite
screen, but I've heard good things about Carada
Good luck, and keep us posted on your progress! This will be fun stuff!