Or the HD7770. It's slightly more than $100 but I recommend it as a minimum for most games now. Here's a good card:http://www.newegg.com/Product/Product.aspx?Item=N82E16814121663
*This card is $120 after MIR but comes with a Far Cry 3 coupon ($60 full price). Hard to beat that!
SIZE OF CARD:
Measure inside your computer but it's likely you'll have no problems.
*I recommend you use FRAPS when starting a game and tweak the quality settings to keep the frame rate as high as possible.
You can even use RadeonPro to:
a) enable VSYNC when not supported in-game
b) enable Anti-aliasing when not supported in-game