First off, the best pet specialization is ferocity, due to the 10% leech buff for you and your pet. This is really good for survivability. Within this specialization, most hunters who want a tanky pet (for soloing dungeons/bosses etc.), choose Scalehides. For example Kodos, Thunder Lizards and Ankylodons. Those come with a special shield ability, granting them 50% dmg reduction for 12s (1min CD).
Other pets can be useful too, some can reduce enemy healing, some slow an enemy (useful in pvp) and some can stealth (cats).
But it generally depends on what you're doing, so you should have 1 for every situation. When you are just chilling out somewhere, you should just choose your favorite look. The cool thing is, that you can also tame rare creatures, granting you a unique looking and a named Creature. My personal favorites are Sunwing (Black Dragonhawk, Burning Steppes) and Umbra'jin (Black Raptor, Zuldazar).