MDF is good for painting but not staining. It also makes a mess when cutting it. Plywood is likely cheaper and looks nice both stained and sealed and painted. It's really up to you - there's no right or wrong. If you are putting artwork and some clear formica/plexi on top I might be inclined to go with MDF because of the smoother surface.
As for the joystick mounting, there are lots of ways of doing this too depending on whether or not you want to see the hardware.
I went with a vinyl covering for my CPs (over both metal and plywood) and exposed carriage bolts. It's just one way of doing it and I think it looks very "clean" ... Here's a pic:

You can clearly see the carriage bolts in the picture on the right. They are screwed underneath with a nut in the picture on the left in the upper corner. You can see bigger construction photos on my website.