After a lot of reading about them, I bought the best projector I could afford (<$300). This was refurbished. It is excellent.
You can see all the specs here: Epson EX3212 Projector
It uses 3 LCD screens -- the light is split with a prism and each color (red, green, blue) goes through its own screen. This looks better than DLP projects that have one LCD screen and then use filters to rapidly project one color at a time.
For the DVD player, I just used the one I had and connected with RCA cables. Only the video line (yellow) has to go from the DVD player to the projector. The audio (white/red) goes to the speakers.
**Updated: There are some other very awesome new projectors, if you are willing to spend a little more. These have HDMI capability, if that is your thing.
This one is expensive, but is wireless: Epson PowerLite 1761W 3LCD Projector
This one is under $400 and has 3D capability: Optoma W311 Full 3D