What do I win?
An awesome-five for mentioning Penny Arcade's On the Rain-Slick Precipice of Darkness.
No, you only get to keep your own equipment, if the new form can wear/hold it, otherwise it is subsumed into your new form. None of the rules state gaining new gear in accordance to your new form.
What about something like a marut? It is a construct, but its AC is largely an armor bonus rather than natural armor bonus - would it appear unarmored? (there is also a spell that specifically changes you into a marut. What about that one?)