Post meteorfall, they're probably mostly on a barter economy. The gang have the useful skill of monster hunting, so they're comfortable. I dunno about 'rich', but they could get by in game by selling off their gear. Afterwards, less so, but they can leverage their combat skills hunting monsters and the like.
A delivery service becomes really important when travelling becomes difficult, and Cloud doesn't have much to fear from bandits, monsters, etc. Bars (and safe bars at that), are also really important in these situations. Yuffie and Red don't need money, Cid is really useful as a skilled pilot and engineer, Vincent can probably get by alone. Barret in one of the novellas hunts monsters I think?