I just rolled my first Altmer mage, a student from a distant land, and I need help with optimizing my destruction spells with certain enemies.

My biggest difficulty right now is battling with the countless Dwemer artifacts, Centerions, Spheres and other mages. So my question is this, what are the most effective spells to use against the Dwemer machinations and what is the best way to go about "mage battles?" It seems like an Apprentice Conjureur is mighty tough for being an apprentice, I mean one-shotting Steadfast Wards and all.

Notice: My mage will end up "rounded," or focussing a little bit in every school of magic, so any other non-destructive magics that will help against the said enemies would be greatly valuable too.

Conjuration to take off the heat. Once you learn to summon Dremora Lord...I'm not sure do you need to fight after that at all
With the mages you could figure out quite fast what type of spells the hostile mage is using. If he conjures something from the oblivion, learn a spell to steal ownership of that demon.
Or if you see that the destruction mage is shooting fire at you cast a fire protection spell and close in and stab him.

conjuration is a must as it can give the mage/bandit/etc you are fighting something else to worry about.
alteration is good for mage armour.
as far as destruction goes, lightning can drain magicka (although i found it quite weak)
frost is good against bandits as it drains stamina
fire works against nearly anyone.
once you get the dual cast stagger perk (something like that) you are good to go.
when it comes to dwemer machines frost is useless, fire works ok as does lightning, but i think i stuck with fire for them

I posted some mage ideas a while ago here, don't know if it is any use: http://www.gamesas.com/topic/1325380-my-almost-pure-mage-and-how-i-play-her/

My approach to pure mage is to almost never take damage. That is why I added sneak. I only use Destruction when (1) I know I can take the guy in a few shots or (2) something is distracting him or (3) runes.

My mage has a 100% decrease on magicka cost, and duelwields Thunderbolt, which deals 90 damage. But when duelcasted, it does over 200 damage. I havn't had to summon a single dremora lord after I got thunderbolt. But, up until you get there, I highly suggest you use conjuration, destruction, enchanting, and perhaps some Alteration.

Magic resistance and conjuration are how you survive while you take out other mages. Well, eventually you can use Paralyze, but alteration doesn't help all that much until you get high up in it.

Destruction can, imho, always use a little alchemical help. Always keeping a few fortify destruction potions around works for me.

My mage felt a lot stronger after I restarted without sneak. At high levels of sneak I'm sure it's powerful, but as a lower level character it was causing me to outlevel my spells, so that when I couldn't avoid combat I was weaker relative to my enemies than I would have been without.