Power Shot-

This is an alarmingly useful perk for any archer.  The time it takes an enemy to stagger is near-universally enough to ready and draw another arrow, possibly two.  Add to this that staggering interrupts whatever your target was already doing, and you have the best possible way to stymie an enemy coming after you.  If they start charging, knock them out of it.  If they start preparing their own arrow, stop them.  If they start casting a spell, interrupt it.  And if you’re shooting from concealment, pump extra shots into them so you can be sure they’re dead before they get the chance to come looking.  Even if you are skilled in melee as well, just cutting down on the number of enemies that make it to arms’ reach is incredibly valuable.  Do you have Archery skill?  Then you want this perk.  Take it.

Ranger-

Depending on how you work your archery, this perk is either vital or useless.  Snipers want to move slower so they can stay stealthed, and without this perk hiding with a drawn bow makes you move slower than any other situation.  While it’s possible to hold down the ‘walk’ button or shift to walking when sneaking up with a drawn bow, that’s extra management you don’t need to worry about when you’re already trying to watch everything, aim, keep your footing good, and make sure that your idiot follower doesn’t give you away.  Those who fire from the open, on the other hand, will find that this goes a long way towards keeping enemies at range while you run backwards away from them and pump them full of... uh... whatever your choice of arrows are made from.  So for a combat archer this is hugely useful, but a sniper will probably want to avoid it.

Quick Shot-

You want this.  Period.  Faster shots is more damage, more chances to stagger, more chances to hit critically, more sneak attacks while stealthed, less enemies closing to melee in combat, et cetera.  Take this perk, take it immediately, take it always.  More valuable than Overdraw, and compounds with everything else that makes any individual shot strong.  Twelve out of ten, would take this perk again and again and again.

Bullseye-

Remember how Power Shot was great because of the staggering effect?  Imagine that instead of staggering your target, you just froze it.  For ten seconds.  The one and only disadvantage to this perk is that a paralyzed enemy falls down, so it can be a little bit annoying to have if you fire primarily as a sniper.  Still, the chance to shut down targets is an amazing boon, particularly as, unlike Power Shot, it doesn’t even care if your target is especially big.  Even better at close range where a lucky shot that triggers the paralyze will often swing a fight dramatically in your favor if not outright end it.  The only reason this isn’t better than Quick Shot is that it only functions roughly one time in seven.  Even so, if you shoot, you want this.