I guess it depends on what type of games you play most - LCD screens aren't all that brilliant at displaying games that have a lot of movement - farcry, UT etc. LCD monitors, when running high speed video tend to "ghost", giving a slihgt blur. The benefit is that pixels are a lot sharper on LCDs than CRTs, and you will hardly notice the blur when watching TV through it.
Edit: It's a while since I've looked at LCD monitors in the shops, they might have improved since, so you're best off going round the shops yourself to check the quality.
I don't know if there are any graphics cards with tv tuners built in, only tv out as far as I know. You can buy a cheap PCI tv tuner for around £30 (don't know what that is in american), but I don't know if these cheap cards have good resolutions.
