Hi, I'm new to wood turning too, and I have the same problem drilling wood blanks for pens. I have resorted to buying pre-drilled blanks as I was getting so upset that i couldn't do it. Only problem there, is that there is very little choice of different matterials.
I tried drilling my first acrylic one the other day.... went fine, followed by a blow out the side, and an off centre one!
I'm using a drill press on god knows what speed (doing it in my lunch break on works machine um!) I am using the bit that all the books recommend for drilling pen blanks tho.
.....so ditto on any tips gratefully received!
Keep at it Heliosuk, such achievement when you finish your first decent pen!!