Firstly I would remove the Staffs own magical ability. It should be an amplifier to the wielders magic. For example, an unarmed mage fires a lightning bolt of 50 damage, using a staff that could get boosted to 60 or more damage, dependant on the staff. This would count towards all magic, not just Destruction.
Secondly, there has to be a tradeoff, boosted magic is a pretty powerful thing. This would come in the form of combat. You could, if you so choose, wield it with both hands and both attack and block fairly effectively, although this wouldn't be as effective as a Claymore or Battleaxe. The other option would be to hold the staff in the offhand while using a Single Handed Weapon, this gives you a bit more attacking power, but blocking would be seriously reduced.
Animation is also important I think. Its what can turn a 'thats pretty' into an 'OMG what did I just do?'. The staff would have to be the focus of the casting animation, and the boost it grants should be noticable visually compared to the stock spell.
I also believe that staffs imparticular should be unique to the player, and it should be something you stick with throughout the game. I was never a fan of 'this one is better than that one' when it comes to weapons and equipment in TES. I've always felt that I could never create the look or style of character I wanted due to the need to upgrade, particularly so as a Mage. There should be different styles available, with subtle pros and cons (damage, blocking ability, extra boosts to particular schools, etc) and it then relies on your abilities to improve in order to deal with tougher enemies. This way your staff becomes as quintessential to your mage as the schools they specialise in. Of course if you do get bored with a staff you can buy a different one, it wouldn't be a one time decision.
Thank you for reading, I look forward to reading any feedback and answering any questions.
Daiyus