[Damian Peckett] has implemented an Apple ][, its 6502 processor, and a cassette port, all on an Arduino Uno. If that wasn’t enough, he also uses a PS/2 keyboard for input and outputs analog VGA.

Then, an Arduino board might be exactly what you're looking for. This open-source hardware platform comes in a multitude of versions, from the classic Uno to the tiny Nano to the powerful Giga ...