Gaming performance is highly dependent on resolution, but remember, you can always run a game at a lower resolution than the monitor's native resolution. So even if you get a 20" or 22" LCD with 1680x1050, you can run your games at 1440x900 or 1280x1024 or whatever your video card can handle and have
(a)scaling the image to fit the screen without preserving the aspect ratio
(b)scaling the image to fit the screen with the aspect ratio intact
(c)no scaling of the image. The image quality will be the best in this case, but there will be black bars around the image.
I would choose (b) or (c) to run games.
Always go for the biggest decent monitor you can afford. Makes web browsing, MS office etc much more enjoyable even if you can't run the games at native resolutions. I am so used to my 24" Dell that whenever I go back to the 13.3" laptop, it feels weird