To clarify about my above post the OP said he wanted one magic school so I would assume he would get the one people said for him to get over the other and he would get other skills, that would not make him a pure mage. If you use anything else other than magic you are not a pure mage. A pure mage with only destruction or conjuration would not be very good at all but I guess it could be done if you want to severely limit a mages potential. My definition or a lure mage is a spell user whip studies and uses only his magic, he learns the science and logic of his craft and learns to control and channel its energies, they will not use mundane means when they can achieve a goal threw arcane means.
Problem is that isn't what you said. Here is what you actually said.
If you do not use all of the schools you are not a pure mage
Those are your words, not mine.
Yep. I rarely used armor or weapons, so my mage was about as pure as any other even though he hardly used alteration (except for light spells) and even more rarely restoration. He was more a
specialist mage rather than a
generalist mage.
Purity can apply to both. In any case, as said above the goal of this style of play is to rarely to take damage or very little. This is a very glass canon (i.e. fragile) build to play, and satisfyingly challenging, especially if you don't abuse enchating and alchemy. I did wear light armor elemental protection boots when fighting dragons, because I didn't want to mess with enchanting... But most of the time went barefoot. The added agility was a BIG plus.

For the first twenty levels or so, I ran around in Necromancers robes. Specializing in mainly Conjuration and destruction. I felt that as a conjurer with only 120 health, it would've been prudent to invest some time in the sneak skill. IMO senaking isn't just for thieves, it's served me well in my pure mage build.
In a play style such as this taking any damage usually ends up in a one hit kill for you, so that's the one thing you really want to avoid at all costs. In my experience, restoration is really good if you have lots of health to spare, but as I stated before, for someone who's only got 120 health, more often than not, it's not going to be of much help on the higher level enemies, more beneficial for the run of the mill bandits you find running around.