As for starting the drill off with a smaller hole, I've started using the long point of my small skew with the lathe spinning and putting the point into the centre of the piece to be drilled and just widening it out a little. I find this gives a good start for the drill.
Paul, I've tried drilling smaller holes then working up the sizes til I get to the size I need, but I find that, when there is not much material for the drill bit to take away that it judders and grabs at the wood or plastic which leads to a greater risk of the blank splitting. Maybe it's just me but that's my experience, so I much prefer to drill with the size it needs first time and take it slow and clear the swarf, even stop for a while to let the drill bit and blank cool before continuing