IMO I've tried the 6200 and it's a pretty low end card, however is true that it's much better than any of the FX, but at the resolution you are trying to game I think you won't be able to go a step higher than min/low-med settings on your gaming purposes.
My friend has a 6600 and he runs games like AOE III, NFS Carbon, at medium settings smoothly, the card may be a little bit over your budget ($80-90), but I've seen it on ebay for about $50, so if you can save a little bit more and find a good reputable seller on ebay I will suggest to buy the 6600.