Here are also some tips about Archery:
Weapon:
Light Bows and Heavy bows are DIFFERENT. They shoot differently and the arrow trajectory is not the same. I find it easier to be on target with a Light Bow. Also, Light bow fires faster. Heavy Bow does more damage per shot, and are better for very long shot
The Bound bow acts like a Heavy bow, as it is designed following the Daedric Bow.
My favorite bow is, for the end game, the Elven bow. It is one the bow with the Highest Dps (the highest being the Hunting bow). The reason is also that I only need to invest 2 points in perks to get Elven Smithing. And with the perk, Fully Upgrade Elven Bow will do more damage than a Daedric Bow upgraded with no perk.
Spoiler: Daedric bow cannot be found in the early game. But if you prefer heavy bow, the Boss in Lost Valkyyg carries an Ebony Bow. You can get him from level 8-10 I think. Also, an Elven Bow can be stolen in Aela the Huntress room at the companion place in Whiterun.
Arrows:
A lot of people are hunting for Deadric Arrows. Yes they are the best arrows (not really. For me the best are the Bound arrows, same stats but free... hehehe).
But remember this: An iron arrow does 10 damage, so 14pts less than the Deadric arrow. Ok, that will make a big difference in the early game. But you cannot find Daedric arrows in the early game. But because arrow damage are added only at the very end in the damage calculation formula, it doesn't benefit from the different multiplier like Overdraw or Sneak Attack, or even potions.
So, in the end game, when your bow is doing 2K+ damage, firing a Daedric arrow will only add 14 damage compares to an iron arrow. LESS THAN 1% differential. At the end, I don't see the point of hunting for Deadric arrows. Finding some is great, but not necessary. i'd rather pickpocket any arrows I can find, regardless of their quality.
Critical:
As I posted one of my earlier post, I find that Critical damage are a joke.
Critical damage bonus are a joke. | Skyrim Forums
I would only take Critical 1/3 in the Archery tree, just because it is necessary to take other perk after. I usually don't even touch the left side of the archery tree though.
Potions:
Always carry Potion of Fortify Archery with you. The max potion you can get +147% potion. That will more than DOUBLE your damage output.
One of the reason I go full Alchemy. poison and Paralyze can be nice too.