so, how do I change which of my pets is my active one?

Since you pinged me, I'll answer:

I honestly haven't changed my active pet ever XD

However, if you just have one sylesti in your party, you just take it out of your party (by clicking 'disband pet' on their pet profile) and choosing a different pet to put in your party (again, on their profile page). Once you have more than one sylesti, you can go to the party menu under explore and move your pets around within the party to make the first one your active pet (or, again, disband and add different pets on their profiles).

Hope that helped!

Thanks!