CPU: AMD FX-8350 4.0GHz 8-Core Processor ($179.99 @ Amazon) The Best AMD processor for the money, 8 cores and can overclock very well.
CPU Cooler: Noctua NH-U9B SE2 37.9 CFM CPU Cooler ($44.98 @ OutletPC) To cool the overclocked CPU of course, but the Noctua brand is known for their quality and very low noise levels.
Motherboard: Asus M5A99FX PRO R2.0 ATX AM3+ Motherboard ($114.99 @ Newegg) Asus is great at implementing high end features even on their entry level boards, and this one will allow you to overclock the 8350 easily.
Memory: Team Vulcan 8GB (2 x 4GB) DDR3-1600 Memory ($68.99 @ Newegg) Because its 8GB has a CAS latency of 9 and its cheap.
Storage: A-Data Premier Pro SP900 128GB 2.5" Solid State Drive ($69.99 @ Amazon) Small SSD with a Sandforce controller for Operating System and vital programs to make the rig snappy.
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($50.40 @ Amazon) Because you're going to need more space than the SSD for all your games and this one is great.
Video Card: EVGA GeForce GTX 760 2GB ACX Video Card ($214.99 @ Newegg) Best GPU in class for the money, there are different variants of the GTX 760 but this one was the cheapest and it comes with Watchdogs free right now. This will determine your game settings for most games, and this card is more than capable within your price range.
Case: Fractal Design Define R4 Blackout ATX Mid Tower Case ($79.99 @ Newegg) Its a clean looking case that has great noise dampening material built in to keep things quiet.
Power Supply: XFX 650W 80+ Bronze Certified ATX Power Supply ($49.99 @ NCIX US) 650watts so if you decide to SLI or Crossfire later (which is supported by the Motherboard) you have room to upgrade.
Optical Drive: Lite-On iHAS124-14 DVD/CD Writer ($12.99 @ Newegg) Just in case you don't know how to install the OS via USB stick, otherwise this is pretty much useless now.
Operating System: Microsoft Windows 8.1 (OEM) (64-bit) ($89.98 @ OutletPC) Its Windows, and you want to play games right.
Total: $977.28 because its less than your budget.