I've read the guides about which elements fit which role, and which stats they need, but I haven't seen anything about which species to use for which element - so, no idea if I messed up there. (I've seen a mention somewhere that species influences stats somehow, but I think all that was said was that Lighiras have really high agility, followed by Luffoxes I think, or maybe it was Bulboris?)

species doesn't affect stats in any way other than that they have slightly varying base stats*- but the base stats don't change how much proficiencies and equips give to a stat.
You can breed, or buy pets that have been bred, or Philter hatching egglings for different base stats.

* The way a pet is made affects base stats, wild-caught being lowest, then reg gen, then enhanced/mythical/starter/exclusive, then exclusives made with stat boosts, with Fabled species having about double what the equivelantly obtained regular species have.

All species have the same max potential base stats if bred** (... except puffadores with mana because there aren't any at all that have over 110mana, wheras all other species can get 120+ one way or another, and there's no way to boost mana in any way when breeding)

**that is, all species can be bred to 2000HP, 100+mana, and 100str/int/dex/agi, now also with possible Grove Bonus stats added in to take the total base calculations over 100


Whatever, you can use any species you like for any element, it doesn't really matter that much

Okay, guess I'll continue assigning elements depending only on what I need and what I think thematically fits.

I have a sort of related question, though: I also seem to remember reading somewhere that among tamed pets, the higher the rarity, the higher the stats. Is that correct?

in regions 1-3, star number correlates with mana (1 star = 60, 2=80, 3=100, 4=120) (fabled species- nephini in region 3, and seasonal fabled and neph in fest zones, have +20 mana on regular species)

Star colour only reflects the number of Trait Points a pet has.


In the Lost Grove- the lv60+ area- however, this is different, and the Grove Bonus stats (the +___ in the base stat bracket) do reflect both the star count and rarity (though those things are related- common and uncommon pets are 2 star, rare+ can be 3-4 stars)
Things that affect the Grove Bonus stat:
Star colour (rarity)
Star number (difficulty)
Themed

Though the exact bonus isn't fixed as specific numbers for any given thing- two pets of the same species, rarity, and difficulty will have different bonus stats, though they will fall within the specific stat bracket.

We have some writing here (scroll down to Lost Grove section of that post) though it only covers the stats of egglings and unthemed pets at the moment.
(the highest bonus I am aware of is this Legendary Themed Luffox. I expect Mythical themes would have stats that fall within the same bracket as the legendaries, as they do with the unthemed pets)