What kind of schools do you combine?
I'm playing an Illusion Mage right now that is working with Destruction as well, so I'm bit curious if at level 10 I should just focus on both schools with fears, destructions while I have my companion with me. Or if I should perhaps invest in a third school already, not sure..
I do sometimes use the Bound Bow with poison but that is only for special assassinations.
I use a little bit of everything, but my main standbys are Destruction, Alteration and Conjuration. In the Illusion school, I mostly use the stealth-type spells (Muffle and Invisibility) as well as a fair amount of the Calm and Pacify spells - those last two are mostly used on beasties in the wild when I just don't feel like battling the 50th Cave Bear or Sabrecat of the day.

But that's for my combat style, which usually involves stealthy approach, use of whatever cover is available, lots of moving around to avoid being hit, and using mage armor and relying on summons for defense/support. My mage is a Breton, so the magic resistance gives her an advantage against other mages - her nightmare in battle is a high level Draugr or Forsworn or Bandit armed with an ebony bow. Those hurt.
For me, the Bound Bow is my primary soul trapping weapon.
It's not the easiest play style at low levels - a sword-and-board warrior or a two-hander will have an easier time when your character is around Level 10, especially if that character softens up tougher targets with a bow before moving in for the kill. But that's mainly because you haven't had the chance to build a decent base magicka pool yet, so you'll keep running out. So you'll want to grab/make whatever potions and gear you can to fortify magicka. Elsewyr Fondues are also great to give your magicka a nice bump for a big battle. And if you're going to play a pure robe-wearing mage, you'll want to max out the Mage Armor perks in Alteration as quickly as you can.
But if you stick with it, your mage can and will be obscenely powerful once you've reached higher levels.