I remove a lot of rust from old Schwinns, and have a step process, depending on the severity.
1-WalMart rust remover, applied with a tooth brush and then a green pad to scrub. Wear gloves. Rinse.
2-Advance Auto Parts chrome wire wheel spray-on cleaner. Spray it on, scrub with a pad, rinse off.
3-Often, by now, the rust is gone, so I wash the bike with a car wash solution that waxes a little.
4-If the rust is still there, I go after it with the fine steel wool and Blue Magic/Mothers/Brasso/etc.
5-If I had to remove rust with the polish, I then apply one coat of Kit wax to try and seal it a bit.
A bench grinder with a buffing wheel is very helpful and saves on knuckles and time, especially on a wheel.
For a lot of the work on a bike, though, the hand is the tool of choice.
Live your life like Coleman did.
1985 Raleigh Racing USA - Competition
1984/85/86? Klein Performance
1988 Centurion Dave Scott Ironman Master
1989 Centurion Dave Scott Ironman Expert
1989 Centurion Carbon R