Intel i5 2700k, Gigabyte/Asus motherboard, ATX preferred, 8GB-16GB (Probably only need 8GB) DDR3 RAM, the 6670 you've been recommended is pretty mid range. I have a 5770 and it's not too great. I know it's a generation behind what you've been recommended, but still, I'd get a 560 Ti if I were you. Don't forget a quality PSU, that's always vital. Something like a 700W Corsair or CoolerMaster.
I'd keep your 3 SATA HDDs and like GSB said get an SSD, 120GB drives are affordable these days. Simply put your OS on there along with any games you plan to play regularly. Use the 3 500GBs for storage.
