You could add another 6670 for XFIRE if you don't get an APU. (i do not suggest getting an apu if you're gonna buy a 6670. grab like a 4100fx, and 1 6670) or upgrade gfx card entirely. I.E. buy like a 7870 or a 7770. once again, if you're gonna buy an apu, don't buy a dedicated gpu. get like the cheapest non apu that'll fit in your build.
just my advice, helped my friend build a similar system for his mom
EDIT: BTW what's your full budget? I'll put you something together. do you need a hard drive and a cd rom? if you have an old comp you can recycle those.
another edit: radeon 7770 is almost the same price as a 6770. much better performance. i kinda guessed on budget and am putting something together atm.