What is the best way to drill smooth 1 1/2 inch holes in 3/4 inch lumber?
I would say use a Forstner bit in a drill press.
A holesaw does a pretty good job, make sure you use a scrap piece on the back too stop blow out.
I agree with both replies. A Forstner will give the cleanest hole and is a good choice is you have a drill press (or a portable drill guide). Be sure to back the speed down. Forstners like to turn slow. The hole saw will do a good job if you take it slow using a hand drill. You may have a little more cleanup work to do afterward. In either case, as Michael said, use a backer board so that you don't blow out the back side.