At 2k you are limited to a few options..
1) SVGA Digital ( LCD/DLP ) projector. These really suck, most of them has poor contrast rates as well as the constant problem with black level in digital PJ.
2) B stock XGA ( nec lt150 ) or used. This would blow all of your budger in one componient and you would not even have a screen.
3) Their is the possibility of some newer Digital PJ down the road that might be easier to use and cheaper ( with lower resolution ). Keep an eye on the panasonic TH-AE100.
4) Used CRT. If you have a progressive DVD player you could get almost any 5.5 or 7" used CRT that scans to 32khz and you would be set for less than 500. Next up would be a unit that scanned to at least 36khz. From there you would look for digital convergance, larger tubes, and lower hours on the units. Things to remeber when looking for CRTs.
a) Buy from a reputable dealer or take your chances. CRT's can be permenetly damaged from abuse.
b) Read up on all of the diffrent models.
c) Must have a light controled room
d) will probably need a HTPC to get the best PQ
e) More worj to install/setup
5) Screw this whole projector idea and get a nice RPTV with much fewer hassles.
Nice thing with the CRT part is that you have options. I would look into basic units like the sony 1031q ( scans to 36khz, analog $500 or less ) or Sony 127x units ( Digital convergance 75khz, 7" tubes, 500-1500 based on condition of unit ). Contact curt palme and get put on the price list that he distributes for his used projectors that he sells.
"Any technology distinguishable from magic is insufficiently advanced" - corollary to Clark's Third Law