If you have the option, make changes with Illustrator.
If you plan to use PHotoshop, 300 DPI should be fine. People can argue til they're blue about DPI, but generally 300 DPI "at size" is considered industry standard.
If you want the overlay to be almost exact, I would recommend going with a reproduction if you can find it. To most people, however, a print of this from a source like classicarcadegraphics.com or mamemarquees.com will do the trick. The price is about 35-40$, and it will feel like an original CPO. Also, if you use classicarcadegraphics, or mamemarquees, just let them know that you are inexperienced, and ask them to make sure it's ready for printing... they probably pre-flight the file anyway, but it wouldn't hurt to ask.