Something like a r3-2200g build you serve that purpose quite well. I recommend some videos by ETA-Prime on youtube that has a lot of emulation content and builds that are good for this kind of use. Maybe start with something like this and customize to fit your use case?
These are US prices using only amazon and newegg.
PCPartPicker Part List:
https://pcpartpicker.com/list/LYb4Hh
CPU: AMD - Ryzen 3 2200G 3.5 GHz Quad-Core Processor ($86.99 @ Amazon)
Motherboard: MSI - B450M GAMING PLUS Micro ATX AM4 Motherboard ($79.99 @ Amazon)
Memory: GeIL - EVO SPEAR 16 GB (2 x 8 GB) DDR4-3000 Memory ($70.98 @ Newegg)
Storage: SanDisk - SSD PLUS 480 GB 2.5" Solid State Drive ($59.99 @ Amazon)
Power Supply: EVGA - BR 500 W 80+ Bronze Certified ATX Power Supply ($50.20 @ Amazon)
Operating System: Microsoft - Windows 10 Home OEM 64-bit ($99.99 @ Amazon)
Custom: 50$ or less case of choice ($50.00)
Total: $498.14
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-05-29 10:56 EDT-0400