Get a Phenom X4 not the X6 above as the low clock speed and difficulty OC'ing with the locked multi sucks for gaming.
If it is out of the 2 original choices though get an i3 as long as the prices are similar.
By spending about $170 for the Intel i5-2300 ($50 to $60 more than an i3-2120) you get a quad-core CPU which won't bottleneck the Graphics card. In this case, he could build his system and maybe buy a better graphics card in two or three years but with the dual-core CPU he'll be bottlenecked.
It wont bottleneck his graphic card because this method just blew most his GPU budget. This suggestion is just un-educated very few people buy a system to be crap for 3 years then add a good GPU when the CPU will be dated You basically suggest he has poor graphics for 2-3 years and an overkill CPU for the GPU he can afford. You know budget gaming rigs are normally run till the wheels fall off then just replaced. Balancing parts is key on a budget making a CPU heavy machine to run games that are largely GPU dependent is just a lame suggestion that smacks more of some blind fanboyism than any educated information.
With the AM3+ platform you get a great upgrade path to Piledriver which in my opinion is worth a lot.
While I think he should by an AMD Phenom II this arguement is dud. Why is PD such a great path? We know its going to be weaker than IB therefore weaker than Haswell which will soon follow it.
Its a budget gaming rig why would anyone get a budget mobo and then in 12 months or less (the period of relevence PD will occupy) get a new CPU?
@OP the build Karmen_bg made above is pretty good for your budget but you shouldreplace the CPU for a Phenom X4 965BE (in my opinion)