If you’ve seen a basic weapon perk, you’ve seen a basic weapon perk.  Anyone that fills things with fletching wants this.  End sentence.

Critical Shot-

Look, another perk copy... right?  Well, no, actually.  It would be if not for the fact that this particular perk improves the damage of the critical shot even further as you take it.  This actually makes it considerably more valuable than the other weapon-based critical perks, because the third rank of it makes your criticals deal scads more extra damage.  That said, the first couple of ranks aren’t that noteworthy- you should probably start taking this perk when your Archery nears 90 rather than early on, so that you can reach rank 3 almost all at once.  Not bad overall, though.

Eagle Eye-

A choice pick for snipers, this can make anything but the most cramped dungeons and the most sudden surprise attacks laughably easier.  Since hiding pretty much automatically succeeds at greater distances, you’ll be pulling off sneak attacks all day and night, and the added zoom makes a huge difference when trying to hit a distant target.  If you shoot things with any regularity, as with Overdraw, you want this.  Unless, for some reason, you’re dead set on firing arrows only at things that are already attacking you (why?).

Steady Hand-

This goes along with Eagle Eye to make sniping a great way to troll your enemies.  Improving your accuracy even more by cutting the chance that your targets have to move out of the way, this perk won’t eliminate the need to lead your target (and if you don’t know what that is, you need to start talking to other people about sniping or even just firing in first person shooter games and come back.  Seriously, it’s a basic skill for this kind of thing.) but it will reduce the amount of lead you need a lot, and give you a lot more chance to aim carefully.  Theoretically, you could try to perform via ‘zen archery’ using instinct rather than aiming, but that doesn’t work very well in a game you operate through buttons.

Hunter’s Discipline-

Since arrows are not craftable in Skyrim without mods, and stronger arrows are rarer, this can be a very, very important perk if you’re running modless.  That particularly applies to people playing Skyrim on a console, but depending on your choice of mods (or not to use mods) on your desktop computer, this can still easily become an important perk for you.  The only people who won’t really care at all about this perk are the ones that use entirely Iron or Steel arrows, since those things are about as common as, you know, hair.