I use a collet based watch makers lathe. Collet chucks will only accurately hold
drill sizes identical with the collet they are designed for, outside this size the jaws are
not concentric with the drill and the the drill will run out of true and will break.
Proops Bros in Leicestershire UK sell a range of microdrills with a 0.125 shaft that
can be relied upon to run true in a standard Dremel collet.
Speed control on my lathe has been achieved by use of a standard high wattage
light dimmer switch in circuit with the (brush) motor.
I also have one built into a electrical twin socket plug box so the controller is one side
and the output socket is along side with the controller plugged into the supply with
a length of 13 amp cable and plug.
Another source of "stepped" drills is from Banggood who supply tungsten carbide
drills with 0.125 shafts for drilling printed circuit (fibre-glass) boards, very sharp
totally resistant to overheating and VERY brittle
Have (accurate) fun!