No one mentioned any of the bear cubs.
I overlooked the bears because their hard hitting move benefits from the target bleeding, but they don't have any moves that cause bleeding. The lack of synergy made them seem weak.
But! Maul does 50% extra damage compared to a basic attack even without the target bleeding, and as you say Hibernate is a very strong heal. Darkshore Cub comes in a 325 power flavor, he's the one I leveled up. I'll admit though that fighting Major Payne is what changed my opinion of bears.
Speaking of best pets, what are your favorite stats to look for?
I also prefer power over speed, in general. The exception would be a pet that has abilities that become more effective when going first (e.g. Evanescence and Dodge, because they dodge two attacks when going first; Kick/Backflip, etc.). If the pet has abilities that deal extra damage when going first (such as Alpha Strike/Pounce/Flurry), then I'd value speed slightly higher, but often the bonus damage doesn't actually make up for the power you've sacrificed to get higher speed. In this case, the various abilities deal 20% more damage than a basic attack when going first, which is the equivalent of having 56 extra power. This is roughly the power difference between picking a breedID 4 vs breedID 5, but the bonus power will always deal extra damage, whereas it's pretty common to run into a faster pet even when you've invested heavily in speed.
On the flip side, in a metagame where everyone values power over speed, it becomes easier to go first even with pets of modest speed. This tends to make speed even less attractive. And as you pointed out, when you beat the opponent's speed by a large amount, you've wasted a ton of your stat budget that could have been health or power instead.
For a healing pet, power is unquestionably king. The only time you'd rather have speed or health is if a fight lasted less than 5 turns: but since you have heals, this is incredibly unlikely.