[Lawtan]

...You're essentially looking for bats, Scansoriopterygids, or the Draco genus of Lizard...

Favorite pet: My black farm cat...that or the Bichir Dragon.

Animal I'd like to have: Either an Accipitridae (Eagles, Vultures), a Axolotl, or a Bat...barring that, a Labrador

Mythical/extinct pet: ...you're asking a person who loves paleontology, biology, and mythology to choose...