Monitor make a difference for Gaming

Short answer = Yes.
If you use a 19" screen then the native resolution is 1280x1024 (i think)
If you use a 22" screen then your native resolution is 1680x1050.
And so on.
If you are looking at benchmarks for games you will see that at higher resolutions the graphics cards have to work a lot harder, expecially if you turn the eye candy on, (anti aliasing, high def shadows, hdr, etc, etc).
So it boils down to the games you play, the size of your screen and your graphics card.
For example I had a 7900 GS and a 17" monitor, it could quite easily handle playing BF2 or LOTRO on that screen, now if I stuck that same setup on a 22" monitor it would have been unplayable as the graphics card couldnt have kept up. Now I have a 4870 and a 22" screen running at 1680x1050 and I can run Crysis on Max settings with a good framerate.
I would go for a 22" monitor (any bigger and even the latest cards struggle with certain games at super high resolutions with eye candy turned on). If you are poor, go for an ati 4670 graphics card, mid range would be the ati 4850, followed by the 4870, with the top end being the 4870x2.
With your monitor go for an LG or a Samsung. You also want to pay attention to the contrast ratio and brightness for the screen (higher the number the better) and the refresh rate, (not more than 5ms for gaming).
Cheers