Well, I'm back to my destructo mage. I'm adding a bit of other magics as well now. Just killed my 3rd dragon, this time all by myself. Conjuration is excellent for keeping it occupied while you regenerate your magicka for the next attacks. :-)
I still don't quite get the shouts, though. I have 2 dragon souls that apparently do nothing, and two words of power that I need dragon souls to unlock. Shouldn't the souls I have unlock the words I have?
[Update: Ah, found it! Another badly documented thing. You need to highlight the word and press R.]
My mage packs quite a punch by now, but still has trouble surviving longer fights, because I tend to run out of magicka, even with highborn and several items that speed up regeneration. Those high-level spells like Fireball and Chain Lightning are very expensive. I'll optimize my spell usage next time, checking which spells cost how much, considering my perks, etc.