I need knowledge regarding this "television" gizmo

I just moved to a new apartment, and I want to put my dinky 13" tv behind me. I’ll probably spend as much time watching DVD’s or on the xbox as watching TV. The breadth of my knowledge regarding modern TV technology extends to the tip of my rabbit ears. My budget is $700 CAN, give or take a hundred or two. Any advice?

Specifically, I’d like to know:

  1. Does being “HDTV compatible” mean anything for consoles or DVD’s?
  2. Any kind of special inputs/outputs I should look for?
  3. How does a widescreen tv impact consoles (I don’t have a console right now, but plan to get an xbox)
  4. Is WEGA or L’Art or whatever worth the money?

Thanks :)