Help me with a 510 pound UK budget build?

Cuts it about as close as possible, but this would be a great build. Does he need a copy of Windows? If not, can get a lot better build!

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: AMD FX-4300 3.8GHz Quad-Core Processor (£78.00 @ Amazon UK)
Motherboard: Gigabyte GA-970A-DS3P ATX AM3+ Motherboard (£49.80 @ Amazon UK)
Memory: GeIL EVO CORSA Series 8GB (2 x 4GB) DDR3-1866 Memory (£60.99 @ Amazon UK)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£38.97 @ Amazon UK)
Video Card: XFX Radeon HD 7850 1GB Video Card (£112.99 @ Amazon UK)
Case: NZXT Source 210 Elite (Black) ATX Mid Tower Case (£39.95 @ Amazon UK)
Power Supply: XFX ProSeries 450W 80+ Bronze Certified ATX Power Supply (£35.98 @ Amazon UK)
Optical Drive: Lite-On iHAS124-04 DVD/CD Writer (£12.99 @ Amazon UK)
Operating System: Microsoft Windows 8.1 - OEM (64-bit) (£80.03 @ Amazon UK)
Total: £509.70
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-01-31 17:51 GMT+0000)
 
Will pretty much max out every game you're looking to play :) Let me know if gaming isn't very important or something, can adjust, but this is a great gaming build for your budget

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: AMD FX-4300 3.8GHz Quad-Core Processor (£78.00 @ Amazon UK)
Motherboard: ASRock 980DE3/U3S3 ATX AM3+ Motherboard (£48.50 @ Amazon UK)
Memory: Patriot Signature 8GB (2 x 4GB) DDR3-1600 Memory (£58.43 @ Amazon UK)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£38.97 @ Amazon UK)
Video Card: Asus GeForce GTX 760 2GB Video Card (£194.40 @ Amazon UK)
Case: NZXT Source 210 Elite (Black) ATX Mid Tower Case (£39.95 @ Amazon UK)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply (£48.91 @ Amazon UK)
Optical Drive: Lite-On iHAS124-04 DVD/CD Writer (£12.99 @ Amazon UK)
Operating System: Microsoft Windows 8.1 - OEM (64-bit) (£77.34 @ Amazon UK)
Total: £597.49
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-01-31 19:04 GMT+0000)
 
Yeah! As for my PC specs

i5 4670k
Sapphire toxic R9 280x
MSI Z87 GD65 Gaming motherboard
2x4 8GB G.skill Ripjaw X series Ram
XFX 750w 80+ Fully Modular PSU
1TB Seagate Barracuda 7200RPM HDD
(Soon to come H100i by corsair! Few weeks Ill get that, So count that was in)
All in one Fractal Design Define R4 pearl black with window.