Welcome to Eldemore, LibreNoctre! It's nice to meet you!
I would recommend setting up a wishlist in the Codex. You can manually select your favorite pets to include by going through the archive section, or you can autofill your wishlist from the wishlist section.
If you'd like to gather up more pets than what you've been able to adopt, checking the giveaways board in the trading section of the forum will help you out!
If you have any questions, please don't hesitate to contact Mira, me, or another member of our staff at any time!