Picking parts for my first gaming PC.

byza

Honorable
If you're willing to build your own, this is a good place to start
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-4690K 3.5GHz Quad-Core Processor (£161.94 @ Aria PC)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler (£24.25 @ Scan.co.uk)
Motherboard: ASRock Fatal1ty Z97X Killer ATX LGA1150 Motherboard (£106.76 @ Scan.co.uk)
Memory: Kingston Fury Red Series 8GB (2 x 4GB) DDR3-1866 Memory (£60.02 @ Amazon UK)
Storage: Samsung 840 EVO 120GB 2.5" Solid State Drive (£59.59 @ Aria PC)
Storage: Western Digital BLACK SERIES 1TB 3.5" 7200RPM Internal Hard Drive (£55.00 @ Amazon UK)
Video Card: MSI GeForce GTX 770 2GB TWIN FROZR Video Card (£227.72 @ Scan.co.uk)
Case: NZXT H440 (Red/Black) ATX Mid Tower Case (£89.99 @ CCL Computers)
Power Supply: XFX 650W 80+ Bronze Certified Semi-Modular ATX Power Supply (£60.06 @ CCL Computers)
Operating System: Microsoft Windows 8.1 (OEM) (64-bit) (£79.11 @ Amazon UK)
Total: £924.44
Prices include shipping, taxes, and discounts when available

Improvements are aftermarket CPU cooler, better PSU, better HDD, includes SSD, better GPU and later model motherboard that has M.2/SATA Express. If it's just for gaming, you don't need an i7.

Note, I didn't include an optical drive because the case I selected doesn't support one, but it does look awesome.

What is your budget, and do you want to overclock?