Intel option... some say the intel are better for gaming.
PCPartPicker part list:
https://pcpartpicker.com/list/mKqJXH
Price breakdown by merchant: https://pcpartpicker.com/list/mKqJXH/by_merchant/
CPU: Intel - Core i5-7500 3.4GHz Quad-Core Processor ($188.59 @ SuperBiiz)
Motherboard: ASRock - B250M Pro4 Micro ATX LGA1151 Motherboard ($75.99 @ SuperBiiz)
Memory: GeIL - EVO POTENZA 16GB (2 x 8GB) DDR4-2400 Memory ($123.93 @ Jet)
Storage: Sandisk - SSD PLUS 240GB 2.5" Solid State Drive ($84.85 @ OutletPC)
Storage: Western Digital - Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($47.84 @ NCIX US)
Video Card: PowerColor - Radeon RX 580 8GB Red Dragon Video Card ($228.99 @ SuperBiiz)
Case: Cougar - Spike MicroATX Mini Tower Case ($38.98 @ Newegg)
Power Supply: SeaSonic - S12II 520W 80+ Bronze Certified ATX Power Supply ($44.89 @ Newegg)
Total: $834.06
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-05-09 17:08 EDT-0400
I would personally go for the Ryzen as its probably best bet for the future.