Well. Congrats. IMO, you have a few options, and your decision will rely on usage and room conditions.
IMO, I know this always happens, sorry to do this to you, but I think the best use of your budget is to expand it by another $500.
http://www.projectorcentral.com/panasonic_ae4000_projector_review.htm
Before you might spring for that, please just wait a couple/few weeks for the release of the Epson 8500. Many will be quite curious about the introductory price after Panasonic introduced the above for 1k less than its predecessor.
For arguably best PQ, while staying at budget, I might advise getting what I have, the JVC RS1 as used. You will see most are asking around $1750, but I'd aim for $1500.
However, I'd only do the JVC particularly, if you will have a bat cave, to take advantage of its native contrast and black levels. No iris used to hit the numbers. The cons are oversaturation of green and red, with nothing you can really do about it. It runs louder than Pana for sure, and I'm assuming Epson as well. This is for the movie buff looking for the most filmic look at the budget.
OTOH, the Panasonic above offers 9 pt gamma correction, which is freakin fantastic for the true videophile, and it's extremely cool that it's offered in a $1,999 unit.
What about used/closeout/refurb?
Yes. Especially refurbs and open-box. Bookmark AVS projector subforum(s), check in daily, and watch for any particular sticky. That's how I got mine, and they sold em out in one single day. (It was $1,500 less than the best prices I found, while still including full mftr warranty).
Used, it is a risky proposition in some ways, but I think it's becoming a more viable alternative. There is a small fleet of nutty videophiles who are upgrading every single year. One guy's post I just read has gone from RS-1, to RS-2, to RS-20, to RS-25. Insane. You can save for sure. The depreciation on these things is very significant.
Right, so the PJ I picked up was for 3k, but let's ignore that for the moment; people were buying that for 4.5k just 1.5 year ago. And I'm already advising you to ask only 1.5k if you get that unit used, or in other words, asking $3,000 less than what the seller paid in 2008.
Still, the 4000u and Epson 8500 are very interesting. I'm now curious how the gamma adjustment compares on the Epson. It's something I wish I had.