first of all you'd have to make an animal feel comfortable living with you (husbandry). it wouldnt despawn, for example. after that you can domesticate it and "work out" different traits, while you have to make tradeoffs. do you want cows (for example) to mainly give milk or meat? high quality or large amount of milk? same with meat. how strong is the cow against diseases?
you could work that out trhough breeding generation after generation, and of course type and quality of food, water, etc.
another example with horses, which will hopefully be implemented soon

do you want a strong horse (pulling carts, carrying stuff, armour) or a fast horse (fast riding) and again, diseases.
what do you think? quite complex, but it could also be easy in the beginning. mind you, iron/wrought/steel is very complex aswell...