89th Wing at Andrews. Interview required to fly with them. Package, including check ride history, flight time history, OPRs, recommendations, etc is sent to them in order to secure an interview. Must have previous major weapon system experience, including lots of aircraft commander time, instructor time, and preferred evaluator pilot time. In other words, most if not all are third tour guys/gals, although I do know a few who passed interview on their second tour with only about 2000-2500 hours of major weapon system time. I don't have the stats on how many were heavy drivers vice jet guys. All are experienced and experts in their past fields. Hope it helps.
Air Force One pilots are "selected" from the best and brightest of the pilots in the 89th. They are usually identified and then given an extended tour, or go to a staff job/school, and come back to the 89th for a second tour before they become part of the Presidential Pilot Office. Just because you get hired by the 89th doesn't do much more than make you a possible candidate. There are AF One pilots that fly each of the aircraft that the President might fly in.
Training depends on the aircraft and the current contract, but initial training is all civilian (except for C-9C, which uses FSI sims but AF flying qual) and then you get to do an AF qual on top of that.
The former Chief Presidential Pilot is now an FO for SWA.