Do you perk all kinds fire, frost and shock or only choose 1 to perk and concentrate on that? And which kinds of damage spells do you favor?

On my mage that focused on Destruction I took all the Augmented perks, but will never-ever take the Intense Flames/Deep Freeze/Disintegrate. They just seem kinda useless to me.
I tend to go with Frost against "Warrior" types, Shock for mages and Fire works pretty well as an all-rounder. I probably like Shock spells the most because they travel faster.

I'd recommend you choose just one & spend the rest of your perks elsewhere. Also, don't bother getting anything higher than Apprentice Destruction, since you'll most likely end up with Destruction Skill enchants on your gear anyway, which makes magicka reduction perks irrelevant.

I'd swear by Flame for the most part... Most damage per MP, and the fireballs are efficient room-cleansers.
But I tend to use Ice Spear against Dunmer and Fire Dragons.... for sorta obvious reasons. Sometimes I just like spamming Ice Spear generally because it leaves these nice glowy spikes through my corpses so I can find them for looting.

oops

only took augmentation perks and perks to reduce magicka cost

I choose fire and shock. Fire is very good for a high DPS and shock is very effective against other spellcaster (drains their magicka). I don't use frost because many of the enemies in Skyrim is immune to frost and with fire and shock spells, frost seems kinda redundant IMO.

If you are using shock damage to drain magicka, you're doing it wrong. You're more likely to outright kill them than drain their magicka to a level where they can't cast any spells.

However that being said, you would be best off just sticking with shock damage magic. There's only one enemy really resistant to shock damage (lightning atronatch) and those aren't too common at all. At the very least, you can rest assured that shock damage will deal its full amount to enemies and not have to worry about resists. And feel free to take a fire spell or two for trolls. Just stay away from frost magic like it is the plauge. In skyrim, just about everything has some natural resistance to frost magic, so it's not going to do a whole lot for you. Even the slowing effect it causes isn't all that good.

I took augmented shock and fire. No need to take them all unless you want to make a pure destruction mage (not really a recommended build ).

I guess but by the time my enchantment skill was high enough to matter I was already into Expert level spells.

Well not irrelevant...after all, you can lower TWO schools of magic to nearly zero (Example: Conjuration for Atronochs and Destruction), but any other spells you cast (Heals, wards, Ebonyskin, Frenzy, etc) will still cost you. It depends on which schools you want to reduce the cost of, and which you just want to use rarely.

I just started a mage and I'm putting the augments into all of them but only taking disintegrate just because I want to play around with shock spells. No, I'm not a pure destruct mage but it is the main means of dmg. I'll use frost for bandits, trolls, anything that is melee. I'll use fire for frost dragons, trolls, and sometimes I just use it for big fights so I don't run out of magick. I'll use shock for mages but most mages I've seen have used shock against me and for now I have to run. Eventually I'll use my other schools of magick and hopefully have enough magick to do something like calm or fear the mages but so far switching between the three is fun and I like choosing based off of who I'm fighting or the situation.

I think I'm doing right. Draining the opponent's magicka while killing him can't be considered wrong. It's the best way so you don't get ice spikes in your forehead. Fire spells is great because of the burning effect and something every mage should have in their arsenal.