If the golden age of arcade video games took place in the early 1980s, then perhaps today we are living in the golden age of DIY gaming systems. Many older computers can be used to run these games, and small single-board computers such as the Raspberry Pi have enough power to emulate arcade games of old for a price under $50.
One challenge though, unless you want to use a keyboard or a standard USB controller, is getting the physical inputs from arcade button to control your emulation software. You could (as I have) attempt to take apart a keyboard and wire the buttons into individual keys. From experience, this does work, but is quite difficult soldering-wise, and multiple button presses can get hairy.
There are also USB-based solutions that allow you to plug wires in which translate data to a computer as an interface device. This works much better, and I wish I’d done some research before destroying a wireless keyboard!
On the other hand, if your platform is a Raspberry Pi, here’s a solution that attaches to it as a HAT, the aptly named “RetroHAT”. The device helps GPIO inputs into keyboard presses, which should be quite useful for getting a cab’ up and running!