What CPU should I get with a GTX 960 on an AM3+ socket?

Boots27

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Dec 31, 2014
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My current CPU is an AMD FX-4130 (quad core 3.8GHz), I've noticed it's falling behind in games meaning i can't use the full ability of the card. An upgrade is obviously due. The thing is I have no idea what CPU I should to pair with this GPU for 1080p gaming! I've thought of an FX - 6350, but i'm also considering the FX - 8350. Should i meet in the middle or am I looking at the wrong CPU's?

Note: Should I also upgrade my mother board from this ASUS M5A78L-M/USB3 to a Asus M5A97 R2.0?

Specs:
CPU: AMD FX - 4130
GPU: Asus Strix GTX 960
Ram: ADATA Gaming Series 8GB (2X 4GB) 1600MHz
Motherboard: Asus M5A78L-M/USB3
PSU: Trust 570W (Soon to be Corsair CX500M)