For a ranged character, there's essentially 3 choices I see...
1: The Ranger has some class skills, but is more build for handling the wilderness, with bonuses to tracking and terrain and whatnot.
2: The Fighter is pure martial prowess with the bow.
3: The Sorcerer/Wizard can supply a lot of VERY nice spells to utilize with the box.
The Rogue is decent, but not really suited for archery, despite what some people may say. A decent dagger, sure, they can WRECK enemies, but with a bow it's difficult to get off sneak attacks.
Ranger is decent, they get an animal companion, a few spells, and lots of utility abilities, like tracking or favored terrain/enemy.
Fighter is where it gets really fun. With a fighter in PF, you get a feat every level, so you can stack up your tricks and get some VERY nice firing support, as well as high BAB advancement and the ability to wear heavier armor - depending on how you play this, you can become a mounted archer taking riding skill and feats, a quick skirmisher using movement related feats, or a pure mobile artillery platform wearing plate armor and composite longbows.
Spellcasters, particularly wizards and sorcerers, can get some VERY powerful abilities if they have the chance to load them up. True Strike gives a +20 to the next attack roll you make. Gravity Bow upgrades your bow's damage by one size category, in this case a 1d8 Longbow becomes 2d6! These are both 1st level spells, and you have access to them immediately, so even ONE multiclass into Wizard and a few Pearls of Power can make a HUGE difference. For 2nd level spells you have access to Enlarge Person, which makes your weapon a size category larger AND stacks with gravity bow for a Longbow to deal 3d6 damage as a Huge weapon! You can further stack this with Bull's Strength for +4 str (Enlarge gives a +2 already) and Deadly Aim, to get something like 3d6+9 damage if you've built a heavy hitter. Or with a Repeating Heavy Crossbow, you could pump out 3d8 x2 (or x3) shots once you start getting Rapid Fire and Multishot and BAB+6 - crossbows have no strength bonus, so you could focus entirely into dex.
One huge thing to note though, is the Archer archtype allows you to perform combat maneuvers through a fired arrow. If you take Power Attack (useless for an archer) you can unlock Improved Sunder (+2 to attack rolls on sunder) and then Greater Sunder, which transfers overkill damage to the wielder of the item. For a 1-handed weapon, like a longsword or rapier that so many enemies tend to use, that's hardness 10 with 5 HP - deal 15 damage and it's destroyed, anything over that is applied to the user. For an axe, that's hardness 5 and HP 5. You start stacking this with damage enhancements to your weapon, or firing particular arrows like the Slow Burn Arrow (1d6 after 1 round, as it explodes) and Clustered Shot, you can start taking a shot at someone's armor, destroy it, and leave them crippled in one strike, with the bomb arrow going off the next round!