You can only tame Beasts, of those you cannot tame all types of beasts, some are untameable. Beast must be of equal or lower level to tame.
Each beast tamed can have different attack styles and after you attain the 2nd lvl of devotion of the beast, you learn these styles and train other pets with them.
So far there are 4 types of styles: Bite, Claw, Cower and Growl.
Bite: Does an added amount of damage. All pets get Bite.
Claw: Does an added amount of damage. Not all pets get this (wolves, thunderwings, PlainStriders don't to name a few).
Cower: Drops aggro from the pet, not really a useful skill that I have seen, as I prefer my pet to hold aggro and if I need it off him, I have special attacks that generate aggro.
Growl: Raises aggro to the pet.
What I have found so far:
Bite: Wolves, Spider types get Bite.
Claw: Bears, Crabs, Scorpids get Claw.
Cower: Not found any yet, not really looking.
Growl: Must be trained at a pet trainer.
There are different levels of these attacks, 5th and up are lvl I, 10th+ are lvl II, 20th+ are lvl III. This is general and not firm as some lower levels CAN have the higher lvl attacks.
So far I am finding the Hunter class to be pretty robust, even without Talents.