You enchant the bow, and then the bow's enchantment gets applied to the arrows as you fly them. You can't enchant arrows yourself.
But there ARE enchanted arrows that you can buy or sell. If you fire an enchanted arrow, the arrow's enchantment is always used, even if the bow has an enchantment on it.
You can also apply a poison. If you have a bow equipped, and then you "equip" a poison, it'll apply the poison to the next arrow you fire with that bow -- and the poison is used in addition to the enchantment, if any.
Marksman is definitely viable. I have a character I've been playing where Marksman is my only combat skill. I usually try to start off things with a sneak attack on a target (you get a bonus for undetected sneak attacks), then I'll summon a creature -- usually a Daedroth -- and then let him go do the melee stuff while I dart around peppering targets with poisoned arrows. I make heavy use of potions -- shield, restore health, restore magicka, as well as poisons, and my character has The Atronach birthsign which gives me a 50% chance of absorbing magicka of spells cast at me (instead of being affected by the spell). So that gives me some good resistance to magicka and a kind of automatic refill. The downside of The Atronach is that your magicka never regenerates on its own, so Alchemy is a good skill to focus on if you choose that birthsign.