I started out with the Emerald Whelpling
, Panda Cub
and De-Weaponized Mechanical Companion
, basically 2 favorites and a third that was nice and a mechanical.
I leveled those through world battles and tamer fight up until the point that I couldn't beat a tamer with just these three. Then I leveled others so that I had one of every family at 25. Pretty much the list that I have as favorites.
Once I was able to beat all the tamers, I leveled pets so that I could beat each of the tamers with 2 25's and a leveler.
At this point, I was still leveling some favorites rather than with any pattern.
Eventually I realized that the tamers gave the best pet XP and realized that vs the higher level tamers I needed to not be level 1 with my leveling pet, so I was also leveling all pets to a target level of 5. I leveled my favorites a little, then leveled them to 25 with a mix of tamers and wild fights. For the tamers, I'd only fight the ones with the bags each day, every day, whether I felt like it or not.
After this I was starting to do pet groupings, like all the TCG pets, all the store pets and so on. Again, I stuck with the target level and a mix of fight types.
Then I decided to get organized. I started rare hunting, and leveling all pets to 5. I started in lowbie zones, and progressed steadily higher until I got to Pandaria. I was also raising pets by family as I finished them (all rare). If I ran out of pets to level in a family that were rare, I'd move on to the next one, but I'd go back and finish it when I got a stone for the non-rare, I but I think this only happened once.
I did Dragonkin, Undead, Humanoids, then Elementals. Once I was down to mechanical, flying and beast, I just leveled them by alphabet.
Once all my pets were 5, I worked on getting them all to 10 and 15. Somewhere soon after I got all my pets to 10, I had all the capture pets as rare, so I focused on areas where I needed stones. I spent a lot of time in the Valley, and finished off my critters faster than I expected. After that I hunted in then Krasarang, but I kinda lost interest once my pets were all 15, so I was doing 2 for 1 stone trades, and buying stone uses from peeps on Lothar.
Once I had all my pets stoned, I stopped doing the non-Pandaria tamers, but I spent a bit of time in Krasarang to get the remaining pets all to level 19 (three tamer fights from 25) and just finished leveling with tamer fights.
Probably way more than you wanted to know.