My first time building a computer

[Macss]

I was wondering if this build would work with compatibility and if there is just anything that doesn't look right for a decent gaming computer. My budget is set to about 600.
CPU: FX-6300
Motherboard: GA-970A-UD3P Gigabyte
Ram: G.Skill Ripjaws X series (2 x 4GB)
Hard Drive: Seagate Barracuda 1TB ST1000DM003
GPU: EVGA GeForce GT 640 4096MB GDDR3
Power Supply: Cougar COUGAR-A760
Optical Drive: ASUS DRW-24B1ST

 

[i7Baby]

Check compatability in PartPicker.

The 990fx mobos are better than the 970's. Especially if you ever want to overclock.

That gt640 won't get you very far. Try a gtx of some sort eg gtx750 at least.

Don't get a Cougar power supply. See - http://www.tomshardware.com/answers/id-1804779/power-supply-unit-tier-list.html#13224310

The best cougar is an s700 and its only tier 2b. Your's isn't even mentioned. Get something from Tier One or Two.

For a pc with a gt 640, you only need a power supply that will deliver 20A on the 12V rail and 350W in total. Try eg a Seasonic G Series 360W