If your going to screw into it you need to go plywood, MDF does not hold screws well. If your going to bolt in your joysticks, which if your a cabinet rocking fool then you need to, it wouldn't matter if your using mdf or plywood.
You can do a lot of other things rather than just painting it, you can use laminate, contact paper, vinyl, arcade control panel overlays, plexi glass. All of those were used in real arcade games.
A plain painted panel is kind of boring. Laminate is expensive and requires more tools to work but is probably the most durable. Contact paper is cheap/fast but can look cheesy and is low on the durability scale. Vinyl is nice easy to work, relatively cheap, and some people like the feel its reasonably durable but doesn't like cigarette burns. Arcade control panel overlays can be expensive but generic ones can be found for a good price, they can look really good, they aren't as boring as a solid color panel, and they were made to stand up to the abuse. Plexi glass is nice because its cheap, easy to work, it allows you to print your own art work to put under it and will stand up to a good amount of abuse.
If you look through the examples section in the faq you will see examples of all of these and probably some other options that I've missed.