If you want to play House of the Dead 3 or Silent Scope Complete, you'll need to purchase a rear projection CRT set, which with your budget you would be able to get a nice TV in the 57" range. Burn-in shouldn't be an issue with CRT, especially in a light controlled area as your basement.
I saw an XBox on a roughly 27" widescreen LCD TV (non-RP, direct view) at a local Frys and thought it looked phenomenal. Not sure what the model number was but it was a Toshiba make. If I had around that much money, I'd probably buy that. I game on a 47" HDTV RPTV, but I'd trade in the size specifically for the brightness and resolution I saw on that LCD TV.
I have my XBOX on my 46" Sony and i'm afraid of the burn in. Since my wife loves that dance revolution game. I want a dedicated tv for the xbox so I don't have to worry about burn in. Hey Carlo does Frys sell new items or refurbished? ( I ask because there prices are so cheap)
Burn in is less of an issue if your TV is calibrated properly. I've read different posts from people who have been playing videogames on calibrated sets for YEARS with no untoward effects.
Frys generally sells new items, but they definitely sell used (returned) items at a discount as well. But yes, their prices tend to be on the cheaper side.
Omard, since you are in the Chicago area, you should also consider Abt Electronics in Glenview Illinois. They will definitely beat any price that Fry's or Best Buy will offer, and I believe they have free delivery into your house. They have a much larger selection than any other electronics store in the Chicago area. I purchased my high def set there back in 1998, and also a high end camcorder from them before that.
Regarding rear projection CRTs, unless the TV is in 'torch' mode, burn-in should not be an issue. Even so, at 50% contrast, I would recommend not playing more than 3 hours of the same game just to be safe. DLP or LCD eliminates this worry, but they have their own issues as price, resolution, black levels and such.
Fry's...scary place. Commmissioned liars, I mean "salespeople"....
Try Circuit City.
If size isn't the most important issue and PICTURE QUALITY is then get the Sony KD-34XBR960. That's what I have XBOX #2 (NOT XBOX 2, my SECOND XBOX) hooked up to. The picture quality is literally the best you can get, hands down. Over double the pixels of LCD.