If you use a hole saw (Lowes or Home depot variety) you can get really nice results if you do a couple things.

1. Buy a hole saw holder with the replaceable center drill bit. Remove the center drill bit and replace it with a (seems like 3/16 or 1/4") smooth rod. This helps avoid the center drill from oversizing the guide hole as you go.

2. Drill the center hole with the appropriate sized drill bit first.

2a. Make a template for the 4 screw holes that centers off the center guide hole. Drill the screw holes before you cut the 2 1/4" or 3 1/8" instrument hole.

3. Once you switch to the hole saw with the smooth rod center guide, place the panel on something like a 2 x 4 with a matching 1/4" hole to keep the hole saw from torquing out of position as the cut starts to make it's way through the last bit of the panel thickness. You may need different shapes of 2 x 4 if you are cutting holes in a corner of the panel.