All three lift a door perfectly well. The difference is noise, maintenance, and how cold your garage gets.
Belt drive
Quietest by a distance. Worth it if there is a bedroom above or beside the garage, and that is most of why we fit them.
Chain drive
Cheapest and toughest, and noisy enough that you will notice. Fine for a detached garage.
Screw drive
Fewer parts, but it does not love a cold Idaho garage without the right grease.