I use a dremel and its workstation.
I've had good luck with a relatively low cost ($90) Harbor Freight bench type drill press.
Also have a Sherline miniature milling machine but with the screw feed, it is hard to tell how the bit is cutting (it has no 'feel') and this leads to 'crowding the bit'. 'Crowding the bit' leads to overheating/breaking.
For blind (no hole) rounded case sides like later DJ etc. I use a 'ball nose' end mill cutter to start the holes because the rounded end does not 'walk' on rounded surfaces like a regular drill bit. After the hole is started, I go with a regular drill bit.
Example of a 'ball nose' end mill cutter...eBay item number: 395664379799