[Cuog]

A worm gear is a commonly used method for a 90 degree gearbox. And they can run in reverse, however they are usually hard to impossible to backdrive. In other words when you stopped applying power the wheels would come to a stop very quickly.

Another option for a 90 degree gearbox would be the gearset used in most angle grinders and angle drills. These use bevel gears and will be easy to backdrive.

Something else to consider is the reduction. Bevel gears will allow reductions similar to normal spur gears like you're used to working with, while worm gears are usually more suited to higher reductions ratios.