The FX 9370, 8350 and 8320 are all the same, just separated by binning and thus clock speed. You'd need to buy a custom cooler to run the FX 9370 and it's price/performance isn't great.
Out of them all the 8320 is the best price/performance, for BF4 it's probably the best price performance CPU out there.
There's also the FX 6300 to consider.
Personally I'd recommend going no lower than the R9 270, it's a big difference from the R7 265 when overclocked and can be had at $180.
Also you could consider skimping on the mobo , getting a 4570/4670 no k at stock, should be fine for a mid end GPU like the 270/270X
well i would be better off with the 8320 which can be overclocked compared to a non K 4670.
Im definitely now consider going the AMD since I have been seeing reviews that the CPU is good on most of the FPS games I play, especially BF4.
thanks for the info though. I really wanted a 4670k cause it really does better on most applications and games, even single threaded ones. but i guess the 8320 isnt bad for the price either