1080p TVs are native 1920x1080. That's going to put SERIOUS stress on a video card, so you better spend big in that category. For the more taxing games, even top-of-the-line $500 graphics is going to struggle to maintain decent frame rates at 1920x1080. You could always run it at a lower resolution and have the TV upscale it to 1920x1080 but you're going to lose some quality.

If all you care about is gaming, best option is probably to get a 720p TV (1280x720) and run your games with all the bells & whistles turned on. Depends on the game, really. If your video card can handle it then obviously 1920x1080 is going to look better, but that's a pretty tall order. If you're going to have to run it at a lower res and upscale then you're probably better off having a lower-res TV and not having to upscale. Of course, then you lose the 1080p for watching HD TV and movies.