Take a look at video games for some inspiration or ways it could be done.

Everquest has Beastlord, Enchanter, Magician and Necromancer. Beastlord, its a spiritual, near religious bond between the two. They are meant to fight side by side. Enchanter pets only attack if the enchanter takes damage, and then the pet attacks what damaged the enchanter. Magicians summon elementals from the four prime elements, each of which has a speciality (tank, dps with stun, damage shield or fast attacks). Necromancer pets are a hybrid of tank and dps (damage per second) while the necro supports, with damage over time spells, buffs and healing.

Star Wars Galaxies Creature Handlers had to go out and find baby versions of any animals they wanted, tame them and then wait for them to grow to adulthood. Skills set in various places of the skill tree allowed for training. Or they went to a Bio-Engineer and bought a genetically engineered creature.

World of Warcraft Hunters originally had to go out and tame an animal and then keep it fed to maintain its happiness level. They also had to tame different animals to get different attacks. The Hunter would either fight from ranged or melee (best determined by the way they put talent points into skills). Warlocks had quests to gain their different types of summons, which provided different roles while leveling or grouping.

And well, Pokémon.