Don't use on-board graphics for gaming.
I'd get an Asus or Gigabyte P45 (or P43 is fine) board, even if its a low end one, and spend a little extra for even a basic PCI-E graphics card. The built in graphics on the G31 etc are really designed for general Windows tasks not gaming.
If you really do not have that option, then I'd go with Asus.
Higher quality of product. It's not just the feature list that's important with motherboards