I've built pretty much the same thing using a RPi3, a USB adapter with two SNES controllers, and a wooden cabinet with two arcade sticks + lots of buttons + another USB interface, with the RetroPie (https://retropie.org.uk/) OS distribution.

It won't play any games newer than say, PS1 (due to CPU limitations and the storage I have available) - but I've got every NES / SNES / Atari2600/5200/7200 / Intellivision / Gameboy / GBA game/ROM ever released, and an older MAME ROM set, all on a 16G SD card with about 9G free.

It will also do some DOSBox stuff and lots of other 8bit platforms that I don't have any ROMs installed for.

RPi: $35ish

SNES controllers: $15 off ebay

SNES USB adapter: $12 off amazon

2-player MAME joysticks/buttons parts kit w/XinMo USB encoder: $55ish off eBay

The most expensive part of the whole thing was the 2-player MAME wooden cabinet (predrilled holes, etc), which was about $75 from an eBay seller.

Display is whatever HDMI-input device I have lying around. Using a 24" monitor at work right now (building one of these for the office lounge).

My grand total: around $200.