What is the best Gaming PC I could build for a

Solution
PCPartPicker part list: http://uk.pcpartpicker.com/p/21KUX
Price breakdown by merchant: http://uk.pcpartpicker.com/p/21KUX/by_merchant/
Benchmarks: http://uk.pcpartpicker.com/p/21KUX/benchmarks/

CPU: Intel Core i5-4670K 3.4GHz Quad-Core Processor (£171.59 @ Aria PC)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler (£23.98 @ Scan.co.uk)
Motherboard: Asus Z87-A ATX LGA1150 Motherboard (£105.44 @ Scan.co.uk)
Memory: GeIL Enhance CORSA 8GB (2 x 4GB) DDR3-1600 Memory (£40.99 @ Amazon UK)
Storage: Samsung 840 EVO 120GB 2.5" Solid State Disk (£73.00 @ Amazon UK)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£46.92 @ Scan.co.uk)
Video Card: EVGA GeForce GTX 780 Ti 3GB Video...
PCPartPicker part list: http://uk.pcpartpicker.com/p/21KUX
Price breakdown by merchant: http://uk.pcpartpicker.com/p/21KUX/by_merchant/
Benchmarks: http://uk.pcpartpicker.com/p/21KUX/benchmarks/

CPU: Intel Core i5-4670K 3.4GHz Quad-Core Processor (£171.59 @ Aria PC)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler (£23.98 @ Scan.co.uk)
Motherboard: Asus Z87-A ATX LGA1150 Motherboard (£105.44 @ Scan.co.uk)
Memory: GeIL Enhance CORSA 8GB (2 x 4GB) DDR3-1600 Memory (£40.99 @ Amazon UK)
Storage: Samsung 840 EVO 120GB 2.5" Solid State Disk (£73.00 @ Amazon UK)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£46.92 @ Scan.co.uk)
Video Card: EVGA GeForce GTX 780 Ti 3GB Video Card (£589.99 @ Dabs)
Case: Corsair 400R ATX Mid Tower Case (£79.90 @ Amazon UK)
Power Supply: Corsair Enthusiast 650W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply (£85.98 @ Scan.co.uk)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer (£12.22 @ Dabs)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) (£65.99 @ Aria PC)
Total: £1296.00
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-11-13 16:58 GMT+0000)
 
Solution

This although a SSD is optional.