I highly recommend a
Forstner bit for drilling holes.
They are a bit spendy compared to other bits, but do a WHOLE LOT better job.
They operate like a pencil sharpener, and shave little curls of wood off as they go.
If you drill a 1/16" pilot hole all the way through, then make about 1/4" deep start on one side, and finish up from the other side, you will get an almost perfect hole.