Are there high scores for collecting? Battling? What? Do they just sit there, storage? I'm not sure what it is for.

For the moment, it's only a storage for your pets. Like a gallery, but you don't take up space of one of your shops if you're only collecting minions. It was in testing for minion battling for a while, but it hasn't been implemented (yet) when the zoo was released.

Lame. Thanks for the answer. Was hoping there would be a collection aspect like plushies or beanbags have.

It was a band-aid for people who had them in large galleries, I think, mostly. It should have some purpose, but it doesn't.