http://skyrimcalculator.com/#114859

Good enough? Some input would be nice.

Basically, I summon a Bound Bow and rely on support magic.

Also, maybe some advice on a race. I narrowed it down to Dunmer or Altmer.

Seems fine to me, a sneak mage with archery instead of destruction i like the idea, as for the race I almost always choose altmer for the magicka boost so i can put the first points in healt or stamina! But is really your choice

You can go even higher...the maximum level is 81, making a total of 80 perks to choose from.

Yeah, but the only reason I didn't do that was because I don't want to become too overpowered.

Is this the case?

I would take that 2 steady hand perk instead of 3 in critical hit.
my archer (normal, not arcane) is a killing machine on master with 3 overdraw, 1 critical hit and no bull's-eye.
but steady hand is very useful, also against flying dragons or other fast-moving folks....

Yeah, I'm only putting one into Steady Hand...Two is too slow for my taste.