This will handle any modern AAA game at 1080p. But I would probably say to press your budget another $40 and go with 16gb of RAM instead of 8gb. But 8gb will satisfy the minimum for any game on the market.
PCPartPicker part list:
https://pcpartpicker.com/list/rwjGYT
Price breakdown by merchant: https://pcpartpicker.com/list/rwjGYT/by_merchant/
CPU: AMD - Ryzen 5 2600 3.4 GHz 6-Core Processor ($164.89 @ OutletPC)
Motherboard: ASRock - B450 Pro4 ATX AM4 Motherboard ($64.89 @ OutletPC)
Memory: Patriot - Viper 4 8 GB (2 x 4 GB) DDR4-3000 Memory ($60.98 @ Newegg)
Storage: Crucial - BX500 240 GB 2.5" Solid State Drive ($38.99 @ Amazon)
Video Card: XFX - Radeon RX 580 8 GB GTS Black Core Edition Video Card ($189.99 @ Newegg)
Case: Deepcool - TESSERACT BF ATX Mid Tower Case ($40.98 @ Newegg)
Power Supply: Corsair - CX (2017) 550 W 80+ Bronze Certified ATX Power Supply ($34.99 @ Newegg)
Total: $595.71
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-01-07 13:13 EST-0500