Why dont the pets have what schools of magic they belong to before purchasing? What are good Myth and Balance pets?
Well they do display the Schools...Only once you have already obtained them :P
There are three good things a pet can do, really: Boost your damage/accuracy/resistance to a certain element, give you a special card to put in your deck, or tertiary, and non-school specific abilities such as 'May Cast' spells and increasing maximum health.
For the boosts in attack and whatever, pets as common as the Krok and Piggle would be good enough for that role. And you can also buy up pets like the Sea Dragon, Fierce Hound, and Sea Turtle which are pretty good for any class who wields them. But I am biased towards pets that give Cards to put in your deck, so I'd suggest the Troll(s), Rat Magician(s), Minotaur, GameStop Piggle(s), Myth Imp (If you can get it), and of course, hybrids.