Talking about the radeons, the 7700 series will run AH well with almost all the eye candy turned on, for 105-125$. Those cards might have 2GB onboard RAM, but they cant really use it, 1GB DDR5 must be enough for them.
The 7800 series will run this game maxed out on 1 full-hd monitor or at medium settings on 3 monitors. The 7850 has an 1GB version for around 170$, but this is a strong enough GPU to take use of the 2GB ram.
I would recommend the 2GB 7850, it has the best price-performance ratio on the market. The HIS one costs 199$ on newegg.