First of all, if you plan to use magic effectively in Oblivion, you should probably ditch the armor, as it reduces your spell effectiveness. It's a problem that will get worse as you level up, so you're better off not being dependent on armor from the outset. The usual remedy is to enchant some clothing with shield effects, and use effects like Reflect to bounce the enemy's damage back on himself.
The exception to that is if you're role playing a "hybrid" type of mage, like a Battlemage or Spellsword, but those are played a bit differently from pure mages.
Secondly, a claymore is not a very effective weapon unless you take advantage of its reach. It's too slow to do much damage over time, which is why mages usually will carry a dagger (preferably enchanted and with poison on it.)
A proper mage is going to try to maintain distance if possible. Targeted spells, conjured "helpers," invisibility; these help the mage to avoid being hit. If you are forced into melee, you can use a weapon like the above-mentioned dagger and cast on-touch spells at the same time. Restoration's Absorb Health is perfect for this, because it hurts your enemy and heals you.
Also, mages usually need two or more different magical skills, paired together. Destruction pairs with Restoration. Conjuration pairs well with Illusion. And Alchemy provides powerful tools from all the magical schools.