Stormwind/Orgrimmar (Human Orphan/Orc Orphan)
- Whiskers the Rat - A strong starting beast, if you've had a really bad run with getting them.
- Speedy - A turtle, nice little water guy with shell protection if you don't have one.
- Scooter the Snail - Snails are always useful, due to the fact that they have a lot of type coverage.
- Mr. Wiggles - A pig, who's a critter, who also has some nice coverage for types.
You can only get one per character per year, but you can jump across all of your alts and such in order to ensure that you get all of the different pets. I believe you only have to be level 10 to do the quests here.
Shattrath - Burning Crusade (Draenei Orphan/Blood Elf Orphan)
- Eggbert - little bird still half in his egg, he's considered a critter and has a couple of cool moves.
- Peanut - A little elephant; he has some good beast and critter type coverage for you.
- Willy - A little demon eye thing? He's kind of creepy But anyway, he has some great magic moves if you need a magic pet.
- Legs - A little marsh walker (found in Zangarmash) that has good magic coverage as well.
Like with Stormwind and Orgimmar, you can get one of these per character, per year.You have to be level 60 in order to do these quests, so you can't do them the minute you get out to Outland (58 for most people).
- Curious Oracle Hatchling - A humanoid with good aquatic coverage, if that's what you need and are looking for.
- Curious Wolvar Pup - A humanoid with good humanoid coverage, if you need someone that has an AoE attack (he has whirlwind, which is pretty handy)
Once again, one pet per character, per year. You have to be at least level 70 to do these quests.
If you're like me and you have all of the pets, then get the Pet Care Package. That little package has all sorts of stuff that can drop out of it, including accessories for your Perky Pug, Battle Stones, and more, so it's definitely worth doing the quests at least once so that you can get some free goodies!
Also, since toys are totally a thing now, you will also want to go ahead and get the Green Balloon as well, which can only be used during Children's Week, 10 silver at vendors.
As for suggestions for pets, of course I want to tell you to get them all, but if you're just getting started and you don't want to do the quests multiple times, I'd suggest getting Speedy or Scooter from Stormwind/Org because of their type coverage; Willy or Legs from Shattrath because they have some solid magic moves that will make life easier, and either of the pets from Dalaran (they're both pretty handy). But, if you have the alts, the patience, and the time, get them all. Or, find them on the AH!
Also, I plan on finishing Part 2 of the Menagerie series when I get a chance later this week. So, if you've been looking for some of the Menagerie challenges that I haven't listed here, then stay tuned and check those out.