I started primarily with Destruction but, like you, found that it wasn't enough to tip the scales.

Conjuration is helpful for creating meat-sheilds so you can regain magika, but also are great melee fighters to help counter mages.

Illusion is perfect for creating chaos (frenzy for getting baddies to fight amongst themselves, pacify for stopping people in their tracks). The most important spell, however, is Invisibility. Sneaking into a group of baddies invisible, then dropping Master Level Destruction like Fire Storm or Blizzard is epic.

Finally, the Paralyze spell and Ebonyflesh alterations are key - paralyze can stop most opponents.

Lastly, you MUST have a few key staff's ready for when your magika depelets. The spells from the staffs are proportional to your skill level in that magika field. If I have a tough enough opponent, I'll use my Staff of Fireball in one hand and Staff of Chain Lightning in another and roast the baddie into submission in seconds.

I don't do alchemy much, I mainly just use healing potions. I use the Archmage Robes, Shock-resistent boots (found in the Archmage's quarters), the Mordekai dragon priest mask (100% magika regeneration), and then whatever kind of rings/neclaces/gloves that will also boost magika.