Additional Traits (APG)Agile ManeuversBlind-Fight: No benefit for ranged combat.
Cloud Step (APG): Here's the deal with this feat. Originally, this gave you infinite Air Walk speed at Monk 20 (since half of infinite is still infinite). People didn't like the Monk being able to at will teleport around the world like 11 levels after the wizard could start doing it, so Paizo nerfed it to cap at 50 ft and be nearly worthless. If your DM uses pre-errata version, keep Slow Fall and get this if starting at or near level 20. Otherwise, swap slow fall out (Qinggong Monk) and ignore this. It can be handy to reach an archery perch...but so is actual flight magic.
Combat Patrol (APG): For a Combat Reflexes build, I could see potential here, but there is a lot I don't like. It requires Mobility and it bases your threatened area on your (medium, since you can't flurry) BAB. On the other hand, it synergizes with your Fast Movement (you don't need to move to shoot your AoOs, but you can choose to move anyway just to adjust the field covered).
Combat Reflexes: Pretty useless pre-level 9, and only really good with some DM houseruling of UC's feats. Available as a bonus feat.
Critical Focus: Bow has an awful threat range, and you'll need high levels to qualify. I'd ignore all Critical feats.
Deadly Aim: The reason you won't have a damage problem. This is your level 3 feat. If you had the +1 BAB to take it at 1st level, you would. In fact,
Mr. Sean K. Reynolds thinks you should be able to take it at 1 and use when flurrying. So, ask your DM.
Defensive Combat Training: The most it'll ever be is +5 CMD. Pass.
Deflect Arrows: If you wait to get Snatch Arrows as a bonus feat at 10+, this gets included for free. Also available as a bonus feat.
Deepsight (APG): Can be quite handy, actually. 120 ft darkvision.
Dodge: Decent in its own right, and a pre-req for some other feats. This is available as a bonus feat.
Elemental Fist (APG): See Stunning Fist. Except, adding 1d6 energy damage to a single attack at level 17 is major weaksauce, so I'd skip this one.
Elven Accuracy (APG): It's like Blind-Fight for archery, with less benefits. Probably a solid reason to pick Half-Elf over Human or Half-Orc if you want this. Improved Precise Shot really limits how much use you'll get from this, though.
Extra Ki: Two extra attacks per day. Yeah, when you say it like that, it sounds much less impressive, doesn't it?
Far Shot: Remember how much this sucked in 3E? Paizo nerfed it for some reason. Yeah... Available as a bonus feat.
Focused Shot (APG): You should be full attacking with a mediocre Int score, silly. Also a bonus feat.
Gorgon's FistImproved Critical: Again, bows. Awful threat range. This is a bonus feat at level 10+.
Improved Initiative: Never a terrible feat, but you gain little from going first compared to a caster or rogue. Even a melee guy values this more to close the gap before someone else can act.
Improved Precise Shot: One of the best archery feats there is! And you get it as a level 6 class feature cleverly disguised as a "choice" of bonus feats.
Improved Unarmed Strike: You got it for free, so enjoy it. *shrug*
Keen Scent (APG): I know it's not in the covered books, but if
Pheromone Arrows are available, this is a powerful feat and makes Half-Orc a good racial choice. For 15 gp a piece, you shoot one at the BBEG and proceed to get a +2 attack and damage against him for the next hour.
Leadership: Broken feat is broken. Even with crappy Charisma.
Lookout (APG): One of the few good teamwork feats, if you and another sneaky PC (or caster) can take this, you will get many more surprise rounds and sometimes be able to flurry during them.
Lunge: If doing an AoO build with a nice DM (see UC feats) AND this boosts your bow threat range, maybe this is
green.
Manyshot: Doesn't stack with flurry. It's available as a trap option bonus feat. How kind of Paizo.
Master Craftsman: A desperate measure of last resorts, this feat priviledges you to burn ANOTHER feat 2 levels later and a whole lot of skill points just to be an inferior Magic Arms and Armor crafter. If the game is "low magic" and has no spellcasters (or they're not willing to help out), I'd play a different class before doing this.
Medusa's WrathMobility: This is also a bonus feat option. You should not exercise that option.
Nimble Moves: Always being able to 5 ft step means never having to say no to full attacking. That said, by level 3 you can shoot someone right in the face, so ...eh. Do not take Acrobatic Steps.
Parting Shot (APG): My lord, those requirements are abysmal! Anyway, this is ok as a bonus feat, the 1/encounter is an odd and annoying restriction. Use it to get out of melee and into the air (if flying) or onto a raised platform or whatever.
Perfect Strike (APG): You get it for free, it's mediocre and definitely a bad trade for Stunning Fist.
Pinpoint Targeting: The pre-reqs are impossible to meet. If you want it, get it as a bonus feat at 10+. Even then, it's mostly just a fallback option for rounds you can't take a full attack or to spice up a readied attack.
Point Blank Master (APG): Another standard issue feat for you. It's still to your benefit to deliver unaswered attacks from afar than to trade attacks up close, though.
Point Blank Shot: Available as a bonus feat. This will either be your 1st level general feat or your 2nd level bonus feat, depending on your plans.
Precise Shot: This is amazing, and WILL be your 1st level bonus feat.
Punishing Kick (APG): See Stunning Fist. Prone makes it harder to hit the foe, but slows his advance nicely. Otherwise, bull rushing is helpful, too. I would take this after Stunning Fist and Touch of Serenity.
Rapid Shot: As with Manyshot.
Scorpion StyleShot on the Run: Godawful pre-reqs, do not take this as a regular feat, only as a bonus feat to ignore them. Even then, you want to full attack, the situations where this is useful but just standing there full attack shooting wouldn't keep you safe are uncommon.
Snatch Arrows: Awful taken as its own feat. Taken at level 10+ as a bonus feat to get Deflect Arrows as a package deal is much more awesome.
Spider Step (APG): The main reason to take this is for Cloud Step. So read the diatribe I left there. If your DM regularly leaves nice archery spots 20-40ish ft off the ground that you can climb to, this might be much more useful for you.
Stabbing Shot (APG): It's a trap!!! You get Point Blank Master at 3 and have unarmed strike before then.
Stand Still: As with Combat Reflexes, needs the level 9 class feature and a kind DM to be useful.
Stunning Fist: Absolutely incredible! ...At level 17. See, all of these "monk" or "fist" feats can be qualified for by ZAM level 11 by BAB, and while you do not gain the improvements a normal monk does, you are still a monk, and thus get the 1/level/day uses, instead of 1/4 levels/day. So, if you expect to get to 17 and beyond, by all means start stocking up on these feats to have a nasty high level full attack with your bow.
Touch of Serenity (APG): See Stunning Fist. Shuts a foe down for a round. Stunning does that and still inflicts damage, making it better, but this is nearly as good.
Vital Strike: Your medium BAB and the fact you can never combine this with the only time you get full BAB (flurrying) makes this and the improved versions horrific for you.
Weapon Focus: You get it for free.
Weapon Specialization: Ditto.
Wind Stance: This requires moving 10+ ft. You will be always full attacking, so this seems incompatible to me.