I'm new to turning and recently decided to make some pepper mills. Starting with squareish stock I roughed the pieces to round and then started drilling several concentric holes of different sizes using forstner bits on the lathe. Somebody gave me the feedback that I should use the largest drill bit first and not to drill any pilot holes. In other words if I need a 1.5" through hole and a 2.5" hole at 1" depth then I should drill the 2.5" hole first followed by the 1.5" hole. This flies in the face of everything I've been taught, but the explanation was that the forstner bits do better without large pilot hole (e.g. from another forstner bit).
In any event I was able to drill the holes into the work pieces, but as I did this I noticed that the drill bit appeared to be wobbling rather substantially (it looked like the work piece was "pulling" the bit such that it wasn't always inline with the axis of rotation. I assume that this is because the drill bit didn't enter the piece perfectly inline with the axis of rotation though for the first ~1.5" I couldn't tell and it looked good). This was especially true when I used a drill bit extension to get the depth I needed (I started swapping in the extension only when I needed it rather than starting with it for deeper holes).
After I drilled the holes I used a cone/chuck to hold the piece in place for sanding/finishing. On several pieces I noticed that the through holes were not concentric with the outer surface of the work piece. In other words when I'd pull the spindle off the lathe I'd notice that the through hole appeared to be at a slight angle relative to the outer surface.
What's the best way to drill a hole that is "perfectly" concentric with the outer surface of a work piece on a lathe? Is it better to drill first and then rough/round? Should I in fact be using a pilot hole? Am I not securing the piece in the chuck properly prior to drilling?