If you plan to hook a computer to it for web browsing and whatnot, go 1080p. If not 720p will suffice.
IMO Plasmas look the best, especially for the space they fit in, however they dont come in sizes bigger than 720p for any reasonable amount, and getting one over 50 inches is going to set you back alot of money.
LCD's are the best value, and look fabulous as computer monitors, also they have no burn in issues, but their contrast tends to be the lowest. I have a 42 Inch 1080p LCD and I absolutely love it.
DLP's are excellent for 56+ inches, however their bulbs are quite frustrating, get hot and take too long to turn on (plus you cant turn the TV on after turning it off till after it cools down. The LED DLP fixes this and adds a better colorspace, but also costs way to much for a 56 inch TV.
LCOS has all the same problems with DLP, but better picture quality in my opinion. Despite my hatred for sony's idiotic business practives lately, I have to say the Sony XBR2 is the best looking TV I have seen in the larger screen sizes.
Projectors are much more complicated to simply state. You can easily get over 100 inches of screen space from a projector, but you also need an amply dark room to place it in. Projectors tend to be something where the more you pay, the better it is, but HD projectors can cost anywhere from 1,000 dollars to 50,000 dollars, so its hard to generalize anything
Overall without a price range, description of the space its going in, and all of its intended uses it is kinda hard to just give an answer (DVD + Direct TV is the ONLY thing you plan to use it for?)