I have some of it figured out, but I need some suggestions.
Please ping me.

Here's how I personally do it:

1. My main party pets, then my lvl 25 team (for the arena), then my 70 team (for later use, currently for missions since i'm nowhere near 70). THen more mission pets (health, strenght,intelligence, dexterity, agility, repeat to the end of the tab)

2. I liked ryos, bulbs, nixis, and qitaris (now not as much) so this is all to them. Except qitaris. Those were mainly in tab 1.

3.I keep my exclusives over here. Plus some overflow

4. More overflow, plus my breeding project.

5. Sales and MORE overflow


You can do it any way you wish, but it's a good idea to keep mission pets within the fist tab or so so you can grab them quickly. And naming your tabs wil definity help.

Its up to you, really.

I personally arranged mine this way:
Tab 1: Party/Exploration Pets, with the name Exploration.
Tab 2: Mission Pets, with the name Mission Pets.
Tab 3: Pets for breeding, with the name Breeding Pairs.
Tab 4: Babies from my breeding pairs, with the name Offspring.
Tab 5: A bit of all the above. This tab is unnamed ATM, but once I get a sixth tab, Ill name this one Breeding Pairs 2, or something like that, and keep my additional breeding pairs in it. My future sixth tab will be called Offspring 2, or something similar.

There are so many ways to arrange things! Some ppl arrange by species, others by time, etc.

Here's how I arrange mine:

Tab1) Mission pets (since it makes choosing mission pets from the drop-in menu easy)
Tab2) Overflow (all the new captured/recently hatched pets go here)
Tab3) My various battle pets (max stat)
Tabs4-6) My favorite themed pets
Tab 7) My breeding projects
Tab 8) Pets for sale

I have since bought or won new stables, and I basically use them as space for breeding projects, or storage for pets (like themed bulboris or regen pets) =P

Thanks for the help! I got some really good ideas from all the posts!