Are any classes better equiped to quest?

As Stereo said, it's movement and range that are most important. I'd say Flame Wizards (the other mages too, but Flame Wizards can make their magic neutral), Night Lords/Walkers, and Corsairs can do it best. Aran don't really have enough range and even though Combat Step is pretty good in most places, it doesn't substitute for raw speed most of the time.

Seconded