I think that the combat machine skill (not catapult) is very useful at the beginning of the game. I only upgrade it for warriors, for example, Thorosar or Christian. It's the best skill for a warrior, especially after level 15-17. It's almost like a separate unit of level 5-6. Also, for a warrior, the following skills are useful:
attack
leadership
defense
archery
ballistics
wisdom (it's always needed)
School of Magic (depending on the circumstances)

As for a mage, I upgrade all magical skills. I make the mage a true mage. He becomes incredibly powerful, although he has many weaknesses, but the main thing is to turn all his weaknesses into advantages.