Okay, here is a build. No way that I could get closer to $500 while still maintaining the gaming performance that you are looking for. And that RAM is a hell of deal, it won't last long.
http://www.game-debate.com/games/index.php?g_id=9210&game=Rust&p_make=Intel&p_deriv=Core+i5-7500+3.4GHz&gc_make=ATI&gc_deriv=Radeon+RX+580+PowerColor+Red+Devil+8GB&ram=16&checkSubmit=#systemRequirements
PCPartPicker part list:
https://pcpartpicker.com/list/CnThLD
Price breakdown by merchant: https://pcpartpicker.com/list/CnThLD/by_merchant/
CPU: Intel - Core i5-7500 3.4GHz Quad-Core Processor ($188.49 @ OutletPC)
Motherboard: MSI - B250M PRO-VD Micro ATX LGA1151 Motherboard ($63.44 @ OutletPC)
Memory: Kingston - FURY 16GB (2 x 8GB) DDR4-2400 Memory ($82.98 @ PCM)
Storage: Seagate - BarraCuda 1TB 3.5" 7200RPM Internal Hard Drive ($45.88 @ OutletPC)
Video Card: PowerColor - Radeon RX 580 8GB Red Dragon Video Card ($229.99 @ SuperBiiz)
Case: Thermaltake - Urban S1 MicroATX Mini Tower Case ($39.99 @ SuperBiiz)
Power Supply: SeaSonic - S12II 520W 80+ Bronze Certified ATX Power Supply ($44.90 @ Jet)
Total: $695.67
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-05-24 09:45 EDT-0400