You can find the top 3 genetics of any horse by looking at the horse's genetics tabs and looking for the 3 highest numbers.

There are some schedules for the different skills in the Breeding forum, but I usually train up the two supporting skills, and leave the primary skill used for competitions low. Leaving the primary low means you can see lower difficulty competitions.

For Shetlands, I train up speed and dressage, then enter low level gallop, trot or jump. Once my wins are in, I finish out the 3 skills as needed