I really don't feel like finding the quote right now, but in a recent interview Yoshi P stated that changing jobs would involve equipping gems or something similar. Though nothing is confirmed, I think it's safe to say that yes, Jobs will use the same weapon types as their parent class.

Job specific weapons have also been confirmed quite a while ago and should(?) be making an appearance in 1.21 when jobs are introduced. It's not known if there will be class-specific weapons, though.