Please review my build!

I would say it is compatible, but I am to 100% sure about graphics card slot, it doesn't state whether it need pcie 3.0 or if kits compatible with 2.0. Sorry I couldn't be of much help. You should probably wait for someone with a bit more experience, sadly these questions tend to take longer to answer. Best of luck and nice build.
 
It would work, but this build is a better run for your money:

PCPartPicker part list / Price breakdown by merchant

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($119.99 @ Newegg)
Motherboard: Gigabyte GA-970A-UD3P ATX AM3+ Motherboard ($74.99 @ Newegg)
Memory: Avexir Core series 8GB (2 x 4GB) DDR3-1600 Memory ($68.99 @ Newegg)
Storage: Hitachi Ultrastar 1TB 3.5" 7200RPM Internal Hard Drive ($48.00 @ Amazon)
Video Card: PowerColor Radeon R9 270X 2GB PCS+ Video Card ($159.99 @ NCIX US)
Case: NZXT Source 210 Elite (Black) ATX Mid Tower Case ($44.99 @ Mwave)
Power Supply: EVGA 600B 600W 80+ Bronze Certified ATX Power Supply ($44.99 @ Micro Center)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($84.98 @ OutletPC)
Monitor: Hannspree HE225DPB 21.5" Monitor ($89.99 @ Newegg)
Wireless Network Adapter: Rosewill RNX-N250PCe 802.11b/g/n PCI-Express x1 Wi-Fi Adapter ($18.99 @ Newegg)
Headphones: Creative Labs Creative Fatal1ty Headset ($27.99 @ Mwave)
Total: $773.89
Prices include shipping, taxes, and discounts when available

I'd suggest to reuse any old keyboard so you can spend more money getting better parts for gaming.
 
While it's compatible it's not very good price or performance wise. The FX-4100(infact the whole x1xx series is horrible for gaming). The CX series of power supplies uses cheap secondary caps that have a short life. You should be getting 2x4Gb sticks of ram instead of 1x8Gb so you get dual channel mode.
PCPartPicker part list / Price breakdown by merchant

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($112.99 @ NCIX US)
Motherboard: Gigabyte GA-970A-UD3P ATX AM3+ Motherboard ($84.99 @ Newegg)
Memory: G.Skill Sniper Series 8GB (2 x 4GB) DDR3-1866 Memory ($84.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($52.92 @ Amazon)
Video Card: Sapphire Radeon R7 265 2GB Video Card ($159.48 @ SuperBiiz)
Case: NZXT Source 210 Elite (Black) ATX Mid Tower Case ($44.99 @ Mwave)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($55.99 @ NCIX US)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($84.99 @ NCIX US)
Monitor: Acer G226HQLBbd 60Hz 21.5" Monitor ($99.99 @ Micro Center)
Wireless Network Adapter: Rosewill RNX-N250PCe 802.11b/g/n PCI-Express x1 Wi-Fi Adapter ($18.99 @ Amazon)
Total: $787.32
Prices include shipping, taxes, and discounts when available