Smithing - How do I improve an item?
Weapons are improved at the grindstone.
Armor is improved at the workbench.
I just want to point out that, for your archer, your "goal" is not necessarily to achieve the highest AR. If you're going to avoid close-range combat almost exclusively, I'd focus on taking any mismatched Light Armor based on the enchantments they have when you discover them. You'll achieve a decent AR anyways, and chances are you'll pick up some "Bows do X more damage" enchants (or something equally useful).