There's been a lot of great advice here, but I think we're getting a bit ahead of ourselves.
If you want to start somewhere, get Mame running. Download some of the free roms and learn how to play them. Familiarize yourself with the keyboard controls, and play a few games with the keyboard. Get a keyboard encoder. I can personally recommend a Kade , an I-pac or the GGG encoders. They just work and all have an excellent support base. Buy a couple of pushbuttons and a Joystick. Don't go crazy here, just pick up something inexpensive from some of the great vendors we have here. Knock a few holes in a plywood box install your joystick and buttons and try a game or two with that. That will get you started, but more importantly, it will get you building. Once you get the first steps down you'll go a little bigger. I would imagine the first project, or even the second wouldn't be the final design, but they'll teach you what your final design will be. Take advice from people here, but in the end it's your's and you're the one who it needs to please.
Regards,
Scam