Yeah, so this Raspberry Pi thing running Emulation Software Retropie.... apparently pretty awesome. My friend made one, and I just ordered and received the parts for one yesterday, I'm beginning to put it all together. It's actually not too hard at all but it takes some time and when you have two kids running around, time is at a premium.
You need a Raspberry Pi 3B (or B+), which is essentially a computer/board, you need a case, you need an SD card to serve as the hard drive, you need a power supply, and a controller. I'd be happy to provide the list of parts I got on Amazon. You can go more or less expensive for all the parts as desired, but you're gonna spend anywhere from $80-$200 roughly. I think my stuff was a total of $130.
Once you get the computer up and running with the software, you have to download games called "Roms" -- but the Retropie software runs/emulates the following systems relatively natively and pain free:
Atari 2600
Atari 7800
Atari Lynx
GCE Vectrex
NEC TurboGrafx-16
Nintendo 64
Nintendo Entertainment System
Nintendo Super NES
Nintendo Game Boy
Nintendo Game Boy Color
Nintendo Game Boy Advance
Nintendo Virtual Boy
Sega 32X
Sega CD
Sega Master System
Sega Genesis
Sega Game Gear
Sega Saturn
SNK Neo Geo
SNK Neo Geo Pocket Color
Sony PlayStation
Sony PSP
Dosbox
ScummVM
MAME (arcade cabinets)
And many others. Not all emulators are pre-installed on Retropie, so it takes some tweaking, but I can provide links to instructions too.
Anyway.... You can find just about any games out there online these days.