Since I am using a sword I feel like I have the flexibility to use ice a bit

In my opinion I'd go with fire. Playing on master with pluto's PISE (precursor to ASIS) I really haven't noticed the slow effect from ice on humanoid npc's near as much on the higher leveled variations (things like Bandit Marauders) I do like the idea of shooting icicles at people but playing pure mage I want to keep my distance. With you not worrying about getting up close and personal this probably doesn't matter much to you, but aside from the initial damage I don't see ice doing anything that fire can't do as well. Lightning is cool too, but the magicka cost is prohibitive and I also seem the have a problem aiming as I've routinely had an enemy dead in my sights but the lightning seemed to pass right through them.

Personally if I had to stay with 1 elelment I'm pretty positive it'd be fire.

Shock is great and I explored that skill in my current game. I augmented it twice and got the Disintegrate perk. It's incredibly powerful. My advice, if you get that perk is, don't use it on dragons. The dragon disappeared, not even a pile of anything left of him so no soul, no loot. Against bandits it's ok because there's still a pile to loot. If my experience was a glitch, someone can tell me. Fire is a great choice and was always my favorite. I loved the sound of dual firebolts leaving my hands. I like ice too for those enemies who are using fire on me. They are usually susceptible to ice.

I bought the Chain Lightning spell lastnight from the wizard in dawnstar and I approached 3 Alik's harassing an unnamed redgard woman. I usually murder the 3 to save the woman but this time I decided to try out my new Chain Lightning spell and holy poop on a stick! It not only killed the 3 Alik's but also the redgard woman all at once! The bolt jumped from body to body! Incredible! Shock is definitely my favorite destruction spell

When I approach them again I will try to record it, and hope to get the same results as I did last night.

I prefer fire first then lightning second. I do like that frost slows enemies down, but in Skyrim there are too many enemies resistant to it.

Visually:

1. Frost
2. Shock
3. Fire

Practicallity:

1. Fire
2. Shock
3. Frost

Fire is cheap (in terms of magicka cost) and works on almost everything. Frost is my favorite visually. I love the way an Ice Spike or Blizzard look. As far as effectiveness though, I'm usually forced to pass on it. The slow effect is great when dealing with melee enemies, but given most of them are resistant to frost - it really cuts down its overall use. Shock spells look great and I love the instant travel. It would be nicer if it actually felt like the additional 50% magicka damage actually felt like it did something against mages. Seems like those bastards have unlimited pools of magicka.

All in all, I typically choose to perk shock and run with it with my mages. I did run a spellsword build with frost as his destruction element of choice and it was a blast. It only really worked because it was my secondary means of damage.