It's impossible to help you much without a BUDGET and telling us exactly what that includes (case, Windows, etc..)
The HD6670 is a very low-end card for a "gaming" build. Even a $100 HD7770 is far better. If you want to game at all, I recommend not using that card (keep for troubleshooting).
Not including Windows, I recommend at least $600 for the case and all internal hardware. If that's not possible, give us a NUMBER and we'll see what we can do.
Be aware:
a) Not all games run well on a lower-end system, but there are many that will run great even on an HD7770. Games like Half Life 2 look and run great on systems that can't even run Far Cry 3.
b) The graphics card is arguably the MOST IMPORTANT part of a gaming PC provided no major bottlenecks exist elsewhere.
c) Building a gaming PC is all about BALANCING THE BUDGET. Too much on the CPU and you don't have enough for the graphics card etc.