I would scarcely call a Dremel precise.
The traditional method with limited workshop tooling and budget, is to mark up the panel, rough cut non-circular holes by a combination of drilling and fretsaw work, then file to exact dimensions. Smaller circular holes should be center punched on the mark then drilled on a drill press with the panel well supported (e.g, by clamping or screwing it to a sacrificial softwood block). A tapered reamer is helpful for non-standard diameters. Large circular holes can also be done on the drill press with a fly cutter, or roughed out with a fret saw then filed to the marked outline. Extreme care must be taken to protect the face of the panel against scuffs, dings and scratches if it is going to be visible.
CAD makes it easier to mark up the panel accurately - one can either do toner transfer, or simply print out a mask for all the non-circular holes, carefully cut them out with an Xacto knife, tape it to the panel as a stencil and mist with spray paint. If using any sort of printout, make sure its correctly calibrated to correct scale distortions.
A nibbler can be useful, but don't push the limits of the material type and thickness its rated for and make sure its blade is easily replaceable and readily available, as sooner or later you are almost certain to snap it.