In your place, I would spend $145 on a HD5750, which is a 3-tier jump, if your resolution is up to 1680x1050. If you play at 1920x1080, $160 for a HD5770 (4-tiers) might be better.
Install that, and see how your performance is. If it is good enough, you're done, for less than half your budget. If your CPU becomes a bottleneck, take a look at what Paul did with an Athlon II X3 in the $750 SBM article. Then get an AM2+ 770 board like this Asus: http://www.newegg.com/Product/Product.aspx?Item=N82E16813131618
for $80, and an Athlon II X3 440 for $85: http://www.newegg.com/Product/Product.aspx?Item=N82E16819103843
for a total cost of $325 + shipping - $10 rebate (if you play that game and win). If you'd rather be certain of getting four cores, then the X4 630 is $100, only $15 more.