So I finally decided to create my first ever pure mage, and well am having a little trouble understanding how a mage works to become extremely powerful in combat so any tips would welcome. Btw this is how mage is right now, race: Altmer, main schools of magic: Destruction, conjuration, alteration, and restoration, and enchanting as well.

A follower early in the game is very helpfull,preferably a good tank like follower.
I played a mage with those same skills as you have.
Conjuration is your best skill you have,use that skill as much as you can early in the game to get good at it.
Cast a summoned creature then use what magick you have left to help out with destruction.

Put all your points into magick so you can keep casting as much as possible.
Those mages robes you get have some very good enchantments on them,wear them.
And don't forget about useing a staff.

Run away from the guy with the Warhammer.