Not that this hasn't been done before, but I'd like to look into it and get some thoughts from others.

Alteration:

-Weighs nothing/Does not slow you down
-Costs less money
-Up to 30% magic resist without enchantments
-One of only three spell absorption opportunities
-Utility other than armor (Water Breathing, Paralyze, etc.)

Armor:

-Can reach armor cap, as opposed to Alteration's 300 rating (or 80% for 30 seconds after a long animation)
-Four enchantment slots with a full set, ten if with a shield and Extra Effect perk
-10% chance to reflect/avoid damage
-Fall damage reduction and Fists of Steel aren't great, but they're there
-No need to cast in the middle of or before a battle (can switch armors any time)
-Not only isn't a magicka drain, but can improve magicka with enchantments

Thoughts and criticisms, folks. I'll edit this post as information becomes available.

Go!

I like alteration for my mage for the reason mentioned above. It is not necessarily cheaper though, as robes can be expensive if you choose to purchase them. I like to keep my distance as a mage, so not reaching the armor cap doesn't bother me. With the Lord stone, you can get an additional 50 armor and 25% magic resistance to add to your stats. That's a perfect complement for alteration. Ironically, magic from other NPC's is my biggest problem, as I can often keep melee characters in check with my illusions and summons. So 350 from ebonyflesh and the stone combined with 55% percent magic resistance, again augmented with the Lord Sone, is more than enough for me. Also, dabbling in multiple schools of magic (Illusion, Destruction, Alteration, and Conjuration) has made me want to use the Arch-Mage robes more than any armor. Also, in regards to casting, if you get the stability perk with dual casting, it will often last through 2 or 3 separate melee encounters depending on how long you fight. Most of my battles last well under 30 seconds.

For my sword and board, nothing can replace heavy armor. Maxing out armor rating is important, but what I find even more important is the resistance to stagger. Stagger is a killer for characters that are strictly melee types (no archery, no magic). Also, I find heavy armor better from the weapons side of things. For a mage, you can go this route too, but in my opinion, a mage that reaches full armor cap with high magic resistance is quite overpowered in that you can stand back, dish out a lot of magic, and not even really worry about dying if you get it repeatedly. I find the cloth mage, makes the game a lot more fun, but to each his own.

Your mention of stagger is another important factor: Heavy Armor users get staggered much less, and shield users even more so (not to mention dishing out the staggering), whereas a clothed mage, regardless of armor rating and resistance, can get staggered pretty easily at the most critical of times.

I'm just trying to idealize an Altmer battlemage here So far, I'm thinking Light Armor.

Armours do not reach the armor cap with just one skill though , you need smithing with it in order to upgrade your light/heavy armours beyond 300/500 ratings , otherwise alteration (which can go way beyond 300 btw , with dragon hide dual cast ) is about equal , you need only 6-7 perks in it to dual cast master spells with it .

Also your armours do not detect life/dead , mass paralyze , absorb magicka passively or give you light etc ... without enchanting it , so that means you also need a 3rd skill to complement armours whereas alteration works indepedently , its a "cheaper" investment in perks for a good benefit , and usually more than enough to breeze through the game iMHO .

Really all depends on your playstyle. If your gonna be up close a lot, then stagger's pretty important. My pure cloth mage keeps her distance and I can count the times I was staggered in one hand. My sword and board (no archery, no magic) melee guy always got into the thick of things, so I was always susceptible to boss's warhammer power attacks. If you're gonna do a little of both, then light armor will probably suit you fine.

Since it's possible reach the armour cap both with light and heavy armour , i personally prefer the light armour because i value the +50% stamina regen better than the less stagger of heavy armour