You're correct: koalas are significantly more closely related to other marsupials, with their closest living relatives being wombats (taking a look at a phylogenesis tree gives a nice little overview). read more
Koala’s are marsupials and as such are more closely related to kangaroos than bears. The term koala bear only came about because koalas look a little like bears. In fact I understand that koalas closest relatives are wombats. read more
Three subspecies of koala have been described, though many biologists believe these distinctions are arbitrary and invalid, so all koalas currently fall under cinerus. Koalas are more closely related to kangaroos and wombats, which are both members of Diprotodontia, than bears, which belong to the order Carnivora. read more