I recommend ditching the tv and get a Full HD PC monitor.
1) Most TV's under 30 or so inches don't actually have full 1080p HD, they just have 720p (its said because you can't tell the difference at the smaller screen size) whereas HD PC monitors of any size come at 1080p.
2) Nowadays most HD monitors feature both HDCP suport and at least one HDMI input.
The only difference between a regular HDTV and PC monitor is that the monitor doesn't have the tv tuner (no cable) although you can purchase an exterior tv tuner later if its really desired. That, and most PC monitor built in speakers suck, but you can easily plug in good PC speakers for cheaps.
If you are looking for just something to game in HD with, I highly recommend. PC monitors are often half the price. You can stay cheap but don't to go with crappy brands like Dynex of Vizio
Newegg had a deal on an HD Asus 24" monitor just he other day for like 170 + 10$ rebate. They always have good deals.
I currently use a Asus 23", my Xbox360 looks gorgeous.