I think the best pets for PvP would be the pets given by a quest (from school teacher). Or if more advanced, in your cause, for ice and storm, the suggestion would be a hybrid. For example, level 48 pets would be Colossus and Stormzilla. If you hatch a pet in the hatchery, it would be a hybrid of storm and ice. Hope that helped! -Alyssa MoonLeaf Level 42 Actually my second school is Storm!
A good battle/pve pet would probably have spritely because you get 300 health and the cast rate is pretty high. Next two talents would be spell proof and spell defy to add on to ice's great resist and boost storm's poor resist. Then paingiver because ice focuses more on defenses so damage would help and storm's huge attacks would be boosted a lot with the extra damage. Finally, another heal ... fairy if you solo a lot and unicorn if you like to play in groups. A great starting pet would be the sea dragon which is actually but it has 3 out of the five talents I stated in its gene pool so it works really well. The drawback is that it's a rare drop from the final celestia bosses and costs crowns to buy. You can get it from the dragons hoard pack but I wouldn't try because it's not reliable. The starfish pet has two of the talents I stated in the gene pool so it's good also (I use it). These are just starter pets and to get the talents I listed, you'll need to hatch with other player for a chance to get those talents in your pet's gene pool.
For player versus player I know less but may cast tower shield, spritely to get rid of weaknesses, dragonblade or may cast balanceblade, may cast pierce to get rid of your opponents tower shield, and energizing battery because it can possibly heal 1,000 and save you. I don't know what a good starter pet is because I don't do pvp but you can just keep hatching with other players to get the talents you want.
Finally, if you want to just train one pet up to mega and use that, I would agree with icepenguin12345 because they have talents that benefit your school and your school only. Sorry for making you read such a long post!