Belt-drive openers are the quietest choice. Rather than using a chain, a rubber belt operates the mechanism. It essentially uses the same components as the chain drive; the only real difference, other than add-ons, is the belt versus the chain.
This is the best choice when noise is a factor. Install belt-driven garage door openers when the garage is under or adjacent to a bedroom.
Averaging $200 to $250, the quieter choice costs about $50 more than the comparable chain-driven model.