OK, now that I have more time than before.

Projectors are very expensive, either to buy or to own.

http://articles.projectorpeople.com/home-theater-tech-news/new-1080p-projectors-compared/

In no case is there a cheap projector that is small AND works well.

$1000 is the baseline cost for a new small projector, and relamping is so expensive that one might actually need to be seated before being told of the cost.

You can try 800x600 projectors, you won't like the quality of the interpolated pixels.

If you buy used, remember that in some cases, these projectors are dumped on the market after being dropped or otherwise mechanically damaged.