Well, Ulm plate is already so good that it is true you don't really need to change it. At later levels in construction you will get better armor, but it is also quite expensive.
On the other hand, it does make sense to give them better weapons, particularly a weapon+shield or two weapons combos. The one that you can forge are much better, and they end up with better defense, protection and damage. Just because he has a halberd doesn't mean he wouldn't know how to wield a sword of piercing and a lead shield, for example...
Or you can give him a missile weapon, so he stays away from the front lines, where bad accidents are known to occur even to Ulmian leaders, and he still has his halberd should anyone come too close. In the same way, knights keep their lance (and hoof) even if you change the rest of the weapons.
So no, equipment *type* does not matter, the leader will adapt (well, putting a full plate on a spellcaster is perhaps going a little too far, he will get tired rather quickly).
For combat leader I tend to enhance survival : protection, defense, a shield, long weapons for repelling, decent damage (killing your opponent is a good way to survive his attack), and whatever useful effects I can find (luck, etherealness, air shield, regen...), more or less in that order. I don't put them in the front line anyway, so they don't need to be able to take 20 heavy infantry and survive, just to take care of straying enemies...
By the way, I won't bother equipping a combat leader unless he has a lot of experience, or a nice heroic ability. If he doesn't, I'll just bring a backup or two along, it is cheaper and just as effective
For a mage, I keep a careful eye en encumbrance. I go for survival too, but in a different way : I go first for the range effects (air shield, magic protection, luck), and for any effect that enhance their power. I slap hand-to-hand defense *** an afterthought : if it comes to that, the rest of my army has not been doing its job.