As you can tell from my posts and tags, I've been through a lot of pets with Tivara. Along the way I've learned some things about my own preferences, and confirmed some things I already knew.
Size and Position. I get easily annoyed when I have to turn my viewpoint or otherwise maneuver to get around a pet, to loot or reach a mailbox or what have you. I've long known that wide-wingspan flying pets just didn't work happily for me. I find that very large creatures like devilsaurs just really don't cut it either. I want my pets lower than me, and not very huge in any dimension.
Damage Dealing. Tivara is Archon's best-geared and most experienced-at-80 hunter. So weird to say that. But anyway, since I'm there, I'm trying to make the most of it, paying much more attention than usual to nuances of Tivara's spec and gear, and also thinking more about just what her pets bring to an outing. As nearly as I can make out, the top dps honors go to devilsaurs and cats right now, and since devilsaurs end up annoying me, Invictus is there to help Tivara bring down as much pain as possible. When he's up to 80, Ørlög will probably get some vacation time with Invictus as my primary all-around utility pet.
(The upcoming changes to hunter abilities and spells, including the large reduction in Volley damage, will undoubtedly affect how I go about endgame farming for leather, meat, and such. Will Sagarmatha at 80 feel like a big farming gain over single-target pets like Invictus? I don't know, and there's no point in guessing. I'll find out when the patch actually arrives.)
Tempering the Exotic. I find, somewhat to my surprise, that overly exotic creatures seem not to work as well for me in the long run. The pets I'm happiest watching in action are the ones that are exotic versions of real creatures, pretty much. No cat actually looks like Invictus, no gorilla like Sagarmatha, but they could, kinda sorta. There's something about the bond to reality that makes the fantasy work better for me.
Oh, and one other note:
Make Mine Bows. Guns often look neat and have good bonuses in WoW, but the firing noise just plain bugs me in short order. So does the silence that comes if I turn off local noises. So I'm happy to once again have a really good bow for Tivara.
This may sound grumpy, but the end result isn't. I'm tooling around with weaponry and pets that perform well and that I find fun to watch, reliably. So it adds up to cool-for-me play.