You don't state if you need: Monitor, OS, keyboard/mouse, Wifi/bluetooth connectivity. This build does not have these, it will hit 50+ FPS on a lot of games at 1080p Ultra. Slap a bit of an overclock on it and you will be at or near your 60.
https://www.youtube.com/watch?v=LZknFkWZNaU
PCPartPicker part list:
https://pcpartpicker.com/list/3z4bsJ
Price breakdown by merchant: https://pcpartpicker.com/list/3z4bsJ/by_merchant/
CPU: AMD - Ryzen 3 1200 3.1GHz Quad-Core Processor ($107.62 @ OutletPC)
Motherboard: Gigabyte - GA-AB350-GAMING 3 ATX AM4 Motherboard ($80.98 @ Newegg)
Memory: G.Skill - Ripjaws V Series 8GB (2 x 4GB) DDR4-3200 Memory ($103.99 @ Newegg)
Storage: Seagate - BarraCuda 1TB 3.5" 7200RPM Internal Hard Drive ($44.89 @ OutletPC)
Video Card: EVGA - GeForce GTX 1050 Ti 4GB ACX 2.0 Video Card ($214.88 @ OutletPC)
Case: Zalman - Z11 NEO ATX Mid Tower Case ($41.20 @ Amazon)
Power Supply: SeaSonic - S12II 520W 80+ Bronze Certified ATX Power Supply ($42.99 @ SuperBiiz)
Total: $636.55
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-02-01 09:42 EST-0500