For gaming, the graphics card is more important than the cpu.
My rule of thumb is to spend twice your cpu budget on the graphics card.
In your case, with a combined $175 budget, I would split it to a $60 cpu and a $130 graphics card.
That would be a $65 Intel G630 and a $130 GTX650ti or 7770.
Lest you think a dual core is a problem, read this article on <$200 gaming cpu's.http://www.tomshardware.com/reviews/gaming-fx-pentium-apu-benchmark,3120.html
The G630 actually competes with the Phenom X6 1090T and bests the X4 980.
You can save a bit on the psu with a Corsair 430W unit for $25 after promo code and rebate:http://www.newegg.com/Product/Product.aspx?Item=N82E16817139026
You do not need an expensive motherboard. Here is one for $45:http://www.newegg.com/Product/Product.aspx?Item=N82E16813157315
I think I might spend a bit more for the better B75 chipset version $55:http://www.newegg.com/Product/Product.aspx?Item=N82E16813157335