Both the drill press and mill/drill may be a bit lacking in sensitivity for such tiny drill bits, Chuck. 0.042" isn't too bad, but a light touch would be needed for 0.020". And if the drill press is an inexpensive model, the quill may rattle about in the housing, increasing the likelihood of bending the bit and breaking it. I had (they are all broken now) some 0.75mm (30 thou) bits with 3mm shanks, which meant that they were easy to grip in a largish chuck which wouldn't have gone down far enough to grip 0.030" shanks.
I used to make my own PCBs for various electronic projects, and only ever used (and broke!) HSS. If you are only concerned with a one-off, an HSS bit with two or three spares to cope with breakages would probably see you through all the holes you need in glass fibre reinforced board.
Andy