I have played as a pure mage before, but have never done the main quest with one. My question: What shouts best compliment a pure mage?

As a pure pure mage, that didn't use armor I found Become Etheral pretty useful for saving my hide somewhat often. Also, Ice Form, Unrelenting Force, Dismay and Disarm were all good shouts to give me time to shoot off some damage while making enemies helpless for a short time. Unfortunately I can't offer advice on Dragonborn shouts since I haven't played it, so there might be more.

Thanks, I haven't played Dragonborn thoroughly yet either. But the shouts you mentioned make sense for a pure mage.

Become Ethernal is probably the most useful one if you plan to use Conjuration.
Even if you don't, it's useful to regenerate magicka, evade attacks and casting Master-Level spells.

Slow Time is very useful in conjuction with destruction magic and it allows you to dodge spells, meele attacks and arrows which can be a life saver later on.
Ice Form can remove meele-enemies temporarly which allows you to back off and focus on archers/enemy spellcasters.

Disarm is also helpful at lower levels, you should get the first two words early on (the last one is quest-locked to the Thieves Guild questline).