If you want to run games like COD2 at 1600x1200, the minimum would probably be a 7800GTX, if you want eyecandy turned up, for recent games, you would most definitly need SLI or 7800GTX 512.
I'm sure the games would look good on it. The thing you want to be careful when buying an LCD monitor for gaming is the Latency. You can't go by the manufacturers rating as it can sometimes be 20ms off. It could be rated for 12ms, but in reality it is 30ms. Check out the roundup of 19in. LCD monitors by Toms Hardware to see what I mean.