Personally, I really like my rare Baby Blizzard Bear for critters, and my rare Luyu Moth for aquatics. Moth will take out 3 Vale aquatics in about 6 hits, and rarely takes much damage.

Bear will do the same for critters, and has Hibernate so I almost never need to stop and heal.

Emperor Crabs are only 4 and 6, actually.

Either really high HP, or high power and high HP. Quite slow, but at 23 mine's shell shield is over 100, and Mists ticks for almost 150 per round.

He rarely drops much, if at all, during fights. I can even solo trios of flying pets with ease.

I've actually been having really good luck getting stones from the pet trainer bags- been able to upgrade my Curious Oracle Hatchling, Baby Blizzard Bear, Peanut and a Molten Hatchling with a breed ID I liked. After hearing the stories of stones disappearing on logging, though, I've been paranoid ab...

Overall stats are modified by the pet and family, as well. Some pets that are type 4 will have much higher atk than another type 4 pet. You have the "base" pet (say, a rabbit). The breed then adds modifiers- 2 to one stat for a 4/5/6 pet, 0.9 to two stats for a 7/8/9, or 0.4 to two stats and 0.9 to ...

I've gotten two stones, both from trainer bags. One from the dozen or so I saved pre-patch, the other since. I'm personally more interested in using them to upgrade my non-capturable pets, but I might break down and use them to get a specific breed ID if I just can't seem to get the breed I want in ...