Light armor for protection and better mobility than heavy. An archer sometimes needs to run.
Archery of course.
One handed for when you close with an enemy. Swords and or daggers.
Smithing for making and improving your gear so you will be self sufficient.
Maybe alchemy. If you are woodswise you should know what herbs are beneficial or harmful.
Sneak for moving steathily through the woods to sneak up on you enemies.
Maybe illusion as a distant secondary. The frenzy and calm spells help, especially for a solo stealth character. Muffle doesn't hurt either if you don't have the enchantment.
Or maybe a Mystic Archer:
-Archery
-Illusion
-Conjuration
-Alchemy
-Enchanting
-Sneak
The idea is to attack from the shadows and avoid direct combat. Use Conjuration for Bound Bow(Awesome Bow, and doesn't need smithing to make it so) and to summon help to attack your foes while you sit back. Illusion for the Silent Casting Perk & the ability to turn foes against each other(The Invisibility & Muffle spells are also great to have). Alchemy to make use of poisons(I'm pretty sure the Bound Bow can be poisoned) and to boost other attributes, such as Archery Damage, Spell Duration, etc.. Enchanting to further boost Character Efficiency. Sneak for obvious reasons.
Like Eniroth, I prefer my archer to back up their bow with magic instead of melee. So, yeah, a no melee mystic archer. Here's my elf's 'major' skills:
Archery - Duh.
Sneak - Duh.
Conjuration - Mystic bow is the only weapon she uses. Conjuring help can be nice as well.
Illusion - Mind control spells are magnificent for starting fights among groups of foes or scaring them out of your face if they get too close. Be aware, however, that using mind control spells effectively requires a very big investment in the
illusion perks, and dual casting the spells helps a lot as well. Quiet casting is also essential.
Alteration - Detect life/undead and 'utility' spells.