Hi Daniel!
Yeah, if I could make my own mandrels and bushings, I'd use the largest size rod for my mandrel I could. Stiffer, and less chance of "whip".
If you're thinking of using a three-jaw drill chuck, as opposed to a three-jaw machinists chuck, for holding the mandrel for penturning, I have found that the drill chucks are not so accurate! But I picked up a neat idea (from Rich K.) who uses a Beall Collet Chuck to securely hold odd size items for turning. He uses it to hold his mandrels, which is nice since he can adjust the length of the mandrel depending on how far it is inserted into the collet chuck before tightening.
I just thought this was the neatest idea, so I bought myself a Beall Collet Chuck, but I was too cheap to buy the collets from them. It uses standard ER-32 spring collets, and I'm just waiting for the right combination of enough money and the best price to pick up an eighteen piece set from 1/8" to 3/4".
Take care!
Scott.