This is the build I made:
What could it play?
You could probably play most games on low to medium settings. You would be able to increase performance by adding a Radeon HD 6770 to run in dual graphics mode with the APU though.
only add a 6670 as a upgrade if you already had the build but if you starting out its not cost effective to do dual graphics
you can see this in my gaming section of this thread
what's your budget and I'll try and see if I can get you a better deal