I agree with Wildcard99, Ryzen CPUs scale well with faster RAM and you don't want to skimp on the PSU.
All of the parts are compatible, but you will get better fps with the i3 8100 over the Ryzen 1200. Until the Ryzen 3 second generation CPUs are released, the 8100 is the go to CPU for budget rigs.
PCPartPicker part list:
https://pcpartpicker.com/list/s4RN6s
Price breakdown by merchant: https://pcpartpicker.com/list/s4RN6s/by_merchant/
CPU: Intel - Core i3-8100 3.6GHz Quad-Core Processor ($118.69 @ OutletPC)
Motherboard: Gigabyte - B360M DS3H Micro ATX LGA1151 Motherboard ($66.99 @ SuperBiiz)
Memory: Patriot - Signature Line 8GB (2 x 4GB) DDR4-2666 Memory ($78.99 @ Amazon)
Storage: Western Digital - Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($43.90 @ OutletPC)
Video Card: Zotac - GeForce GTX 1050 Ti 4GB Mini Video Card ($189.00 @ Amazon)
Case: Cooler Master - N200 MicroATX Mini Tower Case ($29.99 @ Newegg)
Power Supply: SeaSonic - S12II 430W 80+ Bronze Certified ATX Power Supply ($39.99 @ SuperBiiz)
Monitor: Dell - SE2417HG 23.6" 1920x1080 60Hz Monitor ($109.99 @ Newegg Marketplace)
Total: $677.54
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-06-04 10:26 EDT-0400