i was using an old AMD Athlon 64 x2 4800+ (the very old socket 939 version with DDR memory) with a AMD HD 4830 until earlier this month (STUPID CATS BROKE THE GPU AND THE MOBO). I can tell you that the CPU was the main bottleneck, but with the better GPU in i could could play newer games (like Darksiders 2 with out to much problems) a lot better than the AMD 4650 I had in before.
short term i would say go with the AMD 6670, save some money, get a fairly balanced computer
Long term i would say go witha 7770 or a 7790, they are great powerful GPUs that could be used in a future CPU/MOBO upgrade. they come with 1 free game of your choice; NSFW (Never Settle Forever Woot*). Also I will say that the Core 2 Duo is a lot better of a processor than the old A64x2 i was using and will probably work better with the stronger GPU.