Forstner bits, you will mostly use 5/8ths or 1/2 inches, like Lee said, just nip (grind) the tip. You don't really need it for drill press use.
For the table saw, always use a push stick. I make my own from a piece of 3/4" board, as shown here, worn out as you can see, time to make some new! I cut the bottom on the band saw, leaving a 1/4 inch lip to catch the end of my blank, always set the saw to about the same height as the blank.
Not necessary to make them like mine, but it should give an idea
