When I drilled my panel, I did the holes in the wood first and then got lexan. I kind of wished I'd drilled all the button holes at once though, seems like it would have been easier than shoving a hole saw down through an existing hole that was made with a spade bit.
If you mount your joysticks on the top so that the square part sticks through, or if you have a trackball, you'll have to do those square holes in the wood without the lexan attached, so you might do those big square holes before adding the lexan and doing the others. If you're using the score-and-snap method of trimming the lexan to fit your panel, I think that's best done with the lexan firmly attached and possibly bolted down, before any other holes are drilled.