I use a Dremel at its slowest setting (use your smallest burr tip to make a tiny dimple to prevent the drill bit from "walking"). I put on (reading) glasses and get my face in as close as possible, holding the rotary driver with both hands to keep it steady and vertical. At first it is unnerving but quickly becomes easier. Do not be in a hurry. Your eye is probably better than a guide.
I consider a 1/16" drill bit to be perfect because it is slightly smaller than the M2 screw, and so the screw cuts it own way in but remains tight. 1/16" is slightly over 1.5mm so if you are using that bit it will be slightly harder to start but be tighter once in (my guess, I have never tried it with a 1.5mm bit). A 2mm bit might be too big, but again, I have never tried that.