While I've had a genuine Dremel kit for some years now (got it for working on model airplanes), I also have a 1/4" bit Makita regular die grinder, as I used to port cylinder heads in my spare time.
The bits to use for grinding plastic are about the same as ones used for grinding on aluminum: very coarse flutes. You'll have to buy those extra.
If you get a full sized 1/4" die grinder, be sure to get an electronic speed controller, as you don't need to run it at 18,000 rpms all the time. Special 1/4" shank cutters can be found at abrasives supply stores. Most of those cutters have a 4" overall length, but there are some 6" shank bits that are really usefull. Be sure to get carbide cutters, not high speed steel.
And I agree with Dinquey and 'Beard: use a hole saw.