This project was a fun challenge for me, and posed a lot of little dilemmas along the way. In the end I was quite happy with the way it turned out!
Thanks for looking. Enjoy!
Step 1: Top piece
I purchased one 2 by 4-foot panel of MDF in each of the following thicknesses: 1/4", 1/2", 3/4". I also purchased one 2 by 4-foot sheet of 1/8' hardboard. I had plenty of material left over afterward.
MDF is great for things like this. It's easy to cut, shape, and sand, and it doesn't warp, crack, or split like wood (unless it is left out in the elements, or you drill a screw straight into it). Be sure to cut, route, and sand it in a well ventilated area.
If you plan to make one of these, I would recommend finding a real joystick to work from. Measure it and make all your pieces proportional to it.
The top piece is cut from 1/2" material. See photos for details on cutting the beveled edge.