To delve into this a bit futher, would something like the BenQ XL2420T, with the high refresh rate give that higher quality picture?
That is a good monitor for gaming at 24". It's not that you get a higher quality picture from 120hz, but you get a more fluid experience. With FPS over 80 on a 120hz monitor, I find games are much more responsive and eliminate motion sickness I usually experience at lower FPS and refresh rates. It mostly reduces latency, but you can also notice a loss of mild choppiness that you get at lower refresh rates (something you may not noticed until after you get used to more FPS and hz).
It also has a matte screen, something I like, but not everyone does.