I generally play as a ranger/warrior but in my last mage playthrough, I used an awful lot of Alteration and Conjuration magic. Oak/Stone/Ebonyflesh and Conjure Avenging Wraith (Apocalypse - Magic of Skyrim by Enai Siaion) makes my favourite starting spell combo.

Well, my first playthrough i played conjuration and loved it (still do) and the next playthrough i played illusion (bloody hilarious) and the next playthrough Destruction while its the most straightforward way to kill enemies i find that it takes forever to max out (no cheats/exploits) and it also demands a lot of magicka (and thats coming from me with an 850 base.) But to me they're all fun. Although if i had to choose a favorite... i'd probably either Illusion or conjuration, illusion is downright hilarious and practical, but there's nothing like sommoning two dremora lords shouting (the mortal kind) "I honor my Lord. By destroying you!" and then conjuring a weapon of some sort, or even the flaming, exploding familiars. (why are you still reading this?)

For me I go with School of Destruction, mostly because too deal with damage.

I'm not really a dedicated mage, but I do tend to use Restoration spells a lot to heal myself and my companions.

I like conjuration because its a mysterious school. It´s effective when you want to stay secret and storng.

Conjuration, for definite! I've mastered it and have every single spell available except the Flaming Familiar one. My khajiit is a complete badass one-handed (accidentally mastered with no perks...) conjurer that accidentally destroyed Whiterun once because I forgot ash guardians need a heart stone, and whom also always has two Flame Thralls at her/my back. 

~ Sildoyol, Storyteller, She Who Has A Soul Of Fire

The magic school i find the coolest is definetly Illusion, I just love spells like muffle and invisibility, though the one I find most useful is conjuration as it's powers are endless.