Opener: Jackshaft
Jackshaft openers are mounted on the wall to the right or left of your door and connect directly to the torsion bar to raise and lower your garage door. They do not have a belt or chain, so the opener itself is essentially silent. Additionally, because they are not mounted on the ceiling and there is no opener rail along the ceiling, there is no vibration or noise to adjacent living spaces.
Runner up:
A belt drive opener is the runner up for a quiet garage door system. Belt drive openers run on a steel-reinforced belt and are virtually silent. Belt drives are recommended for homes where there is a living space attached to the garage, as they will not disturb any occupants. Because they do have an opener rail attached to the ceiling, belt drive openers will have a slight vibration in adjacent living spaces.