You'll want a tab tensioned screen if you get something pull down/electric lowering. It's pretty expensive compared to a good fixed screen, so I'd rethink that part.
As for the overall budget, you will be perfectly fine. You can get a very good looking 1080P picture starting at about $1k and IMO you can put together a very good budget setup for around $1.3-1.5k now. $3k total can step you up a level with black levels and ANSI contrast. But as with most things in consumer electronics there are tradeoffs with each technology, so stating what is important to you is necessary to really make any better recommendations.