Welcome aboard! Nice little cabinet there.

Is there a spot for start and coin on there?
In my opinion, I wouldn't muck around with trying to fit an atari joystick or other controller in there, You are probably gonna end up needing to butcher the controller or cabinet in the process, and you still will pay money for hardware to mount it in/modify for that cabinet....and you still wont get a super arcade experience.
Getting some used arcade controls is the avenue I would go. Some cheap used happ sticks and buttons should be easy and cheap to come by. I bet there are some arcade collectors around here that are picking those off arcade machines by the dozens. You could also only fill player one controls for now, and add player 2 when you have the money.