This list should help you: viewtopic.php?f=2&t=2978
. As you'll notice, beast, flying and critter have the most uncommon quality pets so you'll most likely benefit most from using your BoE stone on one of those types of pets.
From those three families some pets I might suggest considering for stoning are: P/P Yellow Moth (it's the only moth that comes in this breed), Death Adder Hatchling (S/S breed in particular is a super popular PVP pet), Feline Familiar (I don't use it much myself but it has a mix of abilities which make it strong against multiple families, so is popular with many players).
I personally would not stone any wild caught pets unless they are one of the harder ones to find.
And FYI Zandalari dinos are rare quality by default.