Pine, Birch, Fir, Aspen, Oak, Walnut, Cherry, Luan, Melamine, but no cedar, redwood or boards made of compressed chips. The compressed boards used to use a formalin byproduct or solution with formalin in it, can't recall which, that was not good.
Stain, paint and seal and you'll be fine.
I did build custom cages for a few years using most the materials above. I have not made cages of Cherry or Walnut but know of them and they have been fine. I've still got a couple cages that are probably older than you are that I am still using. Birch was my favorite.