If you've only got room for one damage spell I'd highly recommend Force Pulse from the destruction staff line.
Also when you get to level 15 you'll get the ability to swap weapons which will unlock a second skill bar. You'll have to put your pets on both bars, lest they disappear when you swap, but it will give you room for more abilities. Then you can put your buffs like Thundering Prescence and slightly more situational abilities like AoE on the second bar and switch to it every now and then to cast (I do the same with Surge)
On the subject of AoE abilities, I make pretty good use of them with my Unstable Familiar. What I do is open up combat with a single light attack to get my familiar to get going and draw aggro, as soon as he does I throw down Liquid Lightning and spam Force Pulse, by the time I draw aggro my enemies are pretty much already dead anyway.
*EDIT*I forgot about this since I could never get it to work quite right but are you using the pet attack key? If you can get it to work (I never really could but I'm not a pet centric build so never really tried) it should allow your pets to draw and hold aggro, keeping you relatively safe from damage and allowing you to throw AoEs at people without them instantly running out of it.
For armour, light is better for a mage because of the passives. Increased Magicka regen and reduced magicka cost are always handy, while Medium will offer slightly more armor, none of the passives are quite as useful to a magicka user.

As bigbri said... at level 15 you get a second bar active which will give you more slots to use...

As you are levelling you don't need to worry too much about builds or anything like that... just level & have fun... but here's a few tips:

1. Light armor has better passives for a mage... magicka regen, cost reduction etc so is worth wearing almost all light armor. BUT... wear 1 piece medium & 1 piece heavy as you are levelling... the goal is to level as many skills, lines etc as you can so you can use them later on if you need to. Wearing 1 piece of each of the others will help you level med/heavy too.

2. Force pulse is a very good damage skill to level early on, as is crystal fragments (Which has a knockdown to keep the mobs away). Mages wrath (The execute from storm calling) will be useful against bosses as you gain levels so worth doing as well.

3. Liquid lightning (Morph of lightning splash) is amazing... it increases dps a LOT, but as you say some mobs run out of it. Make sure you level it though if you can as you'll need it to do good damage against bosses.

4. Pick a few skills... put them on your bar.. .level them... then swap them for other skills... level those... swap again... etc etc. There will always be one or two favourites that stay on the bars, but try and rotate a few to level as much as you can, its easier & quicker to do it early on rather than wait until V14 & decide you suddenly need something.

5. Try not to get too hung up an any skill (EG curse) thinking you HAVE to have it on your bar... at your level it makes no difference... when you get to endgame maybe, but early on just use as much as you can, and level as many skills as you can... that's the one & only simple rule

Thanks for the (mostly) helpful tips.
I'll stick with mostly light Armor then and try to swap out skills. Not that easy though...