It's very simple:
1. Balance DEX and STR.
2. Pick up Point Blank Shot, Precise Shot, Deadly Aim, Rapid Shot, Manyshot, Clustered Shots, Improved Precise Shot in that order.
3. For Rage Powers, the most important is Reckless Abandon. It's a big bonus to accuracy and the penalty to AC doesn't matter because you'd be in range. Rest are fully up to you.
4. Find your GM.
5. Pound him (either violently or sexually) until he or she agrees that 15 point buy is a mistake, does not replicate 4d6 drop 1 in any way, allows casters to get 18 on their attribute while penalizing martials who need a more varied selection of stats, and it's only meant for dumb poopoo heads.
go invulnerable barb primal hunter. Get a 16 dex and put your +2 there. Go human for the extra feat. Dump int and CHA to get the stats you need.
Personally I find taking one level of the primal hunter and taking the extra rage feat and then going into another class makes for a better archer. Like barb 1 then fighter or ranger. But I feel a pure barb archer will work fine.
A magical adaptive bow will go a long way, and accounts for those lovely Str stat changes due to rage.
"Fear my anger, for it shall drive the shafts of my arrows deep and true into your weak flesh!"
Also, if you were looking to do something just a bit different, you could always be an atlatl archer, though the damage output is a bit less, d6 vs d8 of a long bow, there is no cost to adding Strength to damage, plus, atlatl's cost very little, but benefit from ranged feats same as a bow would.