All want access to Soul Trap (Apprentice in Mysticism) and to maintain their enchanted gear (Journeyman in Armorer) so they get built to hit those as soon as possible. When I tried to make a pure mage that didn't need them, I discovered that the game won't let me get away completely, as you can't block without an item that needs repairing (shield, weapon or staff) and hand-blocking is much less effective. Enchanting clothes instead of armor gets around the need to repair that, and using Sigil stones to enchant can substitute for Soul Trap, but only if you let the gates open.
Most of the characters have maxed out strength and endurance early, so that has meant Armorer/Block/Heavy being raised, as well as one or more of Blade/Blunt/H2H. So I've tried to make characters that didn't need those, and of course they were poor (can't haul out the loot to sell) and died easily until they got a lot of defensive gear (which had to be light!)
Some of the problems can be alleviated with mods (e.g. Bag of Holding mods that let you carry stuff beyond your encumbrance, unlimited rings or amulets) but I haven't done that to any significant extent.
What has everyone else done? And are there any other attributes/skills you can't do without?