For ease of setup you want horizontal and vertical lens shift.
Here are some of the attributes that separate the projectors in the 3k and under category
First thing is to see if you are sensitive to RBE. If you are, then you need a DLP with a fast color wheel or you need to go with LCD. This will narrow your choices considerably so figure out if you're RBE sensitive.
3D - DLP is basically ghost free, some LCD projectors are close to ghost free, brightness matters here (the brighter the better, the glasses cuts off a lot of brightness)
The JVC LCOS like the one mentioned above are great at 2D, but I hear they aren't as good at 3D material so you have to decide how important 3D is to you. That will narrow your choices considerably.
Motorized lens with memory. This is for CIH setups, the panny 8000 has this ability, it's a popular choice for those that want a CIH setup.
The sony HW50es is a top contender for all around projector. Some say the JVC RS46 beats it by a little bit in terms of 2D but the JVC has more ghosting and doesn't have the brightness of the sony for 3D.
A cheaper projector that is good for all around use (3D, 2D, light gaming) is the epson 5020/5030. It's a bit more than the panny 8000 but less than the JVC/Sony ones.
Popular brands here at avs seem to be:
Sony, JVC, Epson, Benq, optoma
If you're doing a legit dedicated theater, I'd go with a real screen instead of painted on. If you're doing a fixed frame screen, it's not that expensive considering all the other gear and the cost of furniture. Look up jamestown av in your search engine.
Yes a new processor is worth it, if only for the inputs/outputs. Also if you want 3D, it's easier if your receiver can handle it, or else you need 2 hdmi connections from the bluray player. Also if your processor can't do HD audio, it's well worth it.
The projectors I'm currently looking at are the epson 5020/5030 for all around projector (3D, 2D, gaming) at the 2k-2500 price range. Sony HW50ES (I can't afford it, but if I had 3k on a projector...I'd get this one). Projectors in the 1500 price range, although better than my optoma gt750....it would be too much of a lateral move IMO. I'd rather save the money.