My monitor is 37" but that doesn't matter because it's only 1920x1080.
Which is what we actually need to know...
Size means nothing, higher resolutions require a better video cards.
Personally I just bought an "MSI 7850 2GB OC TwinFrozr" and love it. I can max out most games on my monitor (at 1920x1080) but I'm not the kind of person to pitch a bunch of money at a video card. I paid $165. Some video cards make mine seem fairly cheap.
If you want top end I wouldn't do more than a 7970.