I'm building one soon for a similar price. Specs are:
Intel I7 4770 Processor
Nvidia GTX 970 Graphics Card
16GB 1600mhz DDR3 Corsair RAM
2TB ST2000DX001 SSHD
H97 PRO Motherboard
Hyper 212 Cooling
XFX 550w PSU
Logitech M185 Wireless Mouse
Logitech K120 Wired keyboard
For the cooling just make sure your case has a width of 160mm or above because the fan has a width of 120mm and it has to be mounted on a motherboard.
It's a good all round setup and should hand'e most games quite happily on full settings, and if you want frame rate instead it will easily achieve 60+ on most games (provided you don't mind some lower graphics). It also is pretty well future proofed. The gpu can run Direct X 12, the ram should be more than enough for anything, and the power supply means that you can upgrade to a more powerful gpu later if you wish.
The keyboard and mouse are quite basic. If you want a gaming mouse then I can't help you there.
If you want to buy pre-built then I would suggest this -
http://www.pcworld.co.uk/gbuk/desktop-pc-monitors/desktop-pcs/gaming-pcs/pc-specialist-vortex-inferno-gaming-pc-10109327-pdt.html