Something like this should suffice for what you need, it should be more than enough to run said games at high resolution on max settings @60fps, although it's hard to say for BF4 because the optimisation is a mess.
I haven't personally used all the parts in this build however, so you may want to read some reviews and get some second opinions, this build is a lot cheaper than your budget but should still be fine, if you want to save even more money you could get a 250gb ssd instead of a 500gb, and a fx6300 instead of an fx 8350, also a cheaper case would work fine, I simply like this case and your budget allows it. This case also comes in other colours, such as black and red, black and blue, black and green, etc.
This case however isn't too good for air cooling, it will work, but it won't have that great aiflow so if you wanted you could look at getting watercooling for your system, I've never used watercooling so I can't help you there I'm afraid.
Any questions about the build just ask!
PCPartPicker part list:
http://pcpartpicker.com/p/CxNkgs
Price breakdown by merchant: http://pcpartpicker.com/p/CxNkgs/by_merchant/
CPU: AMD FX-8350 4.0GHz 8-Core Processor ($174.99 @ NCIX US)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($29.98 @ OutletPC)
Motherboard: Asus Sabertooth 990FX R2.0 ATX AM3+ Motherboard ($170.27 @ Amazon)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory ($89.99 @ Amazon)
Storage: Crucial MX100 512GB 2.5" Solid State Drive ($218.46 @ NCIX US)
Storage: Western Digital BLACK SERIES 1TB 3.5" 7200RPM Internal Hard Drive ($74.50 @ Amazon)
Video Card: XFX Radeon R9 280X 3GB Double Dissipation Video Card ($259.99 @ NCIX US)
Case: NZXT H440 (White/Black) ATX Mid Tower Case ($109.99 @ Newegg)
Power Supply: Corsair CX 600W 80+ Bronze Certified Semi-Modular ATX Power Supply ($54.99 @ Newegg)
Total: $1183.16
Prices include shipping, taxes, and discounts when available