Your first thought, doubtless, is Elven Ranger!
Don't do that.
In the first place Legolas is not a Ranger, he's a Fighter. In the second place...just don't do that.
But I am HERE TO HELP. Of course I am. Helping is what I do. Noblesse Oblige and all that.
Leaving race choice out of it for the moment (or entirely really because I don't care what race you play) you have two choices in class if you want to go the archery route: Fighter and Ranger. Technically any class with access to Martial Weapons can use a longbow but you want to make this your focus, so we are going to stick with the two I have mentioned above.
What are the benefits of each?
RANGER-Rangers get a slew of cool abilities, including wilderness survival, favored enemies, and magic spells (at level 2). At level 2 they get to choose a fighting style and at level 3 they get an archetype (hunter or beast master), with the preferred archer style being Hunter. By selecting your Hunter abilities carefully and Archery at 2nd level and keeping your Dexterity high, you can be a deadly archer indeed.
But why would you do that?
Oh, because you are confused about what the word Ranger means. MMOs are much to blame for this. Somehow Ranger went from its original meaning (one who ranges, that is moves about the open land in an independent manner) to its new MMO inspired gaming meaning (one who attacks at range/with ranged weapons). Well that's bollocks.
If you really want to be an archer you need to look to the Fighter.
FIGHTER-Fighters have access to all the weapons and armor available, gain a Fighting Style at 1st level and gain many abilities that make them ideally suited to their name-sake calling, which is fighting. If you want to catch food, you are a hunter. If you want to cause the enemy to catch death by a goose, you are a Fighter.
Now despite the fact that Dexterity controls shortbow and longbow attacks (vice Strength, which should be the operative ability given how much training and chest power is needed to pull a bow effectively) it need not be your highest or primary ability to become an archer. Allow me to elucidate.
The Fighter has many options. Focusing on Dexterity can certainly improve your attack and hit bonuses with ranged weapons, and that makes a high DEX an attractive option for an archer but a quiver only holds 20 arrows. You are only going to recover about 50% of them per combat. Large or particularly tough monsters will take many arrows to stop and if they charge into your face you won't be doing much shooting with your bow. You need some melee skills if you expect to survive. The options for finesse weapons (those weapons that can use DEXTERITY for attack and damage bonus) are somewhat limited. The highest damage finesse weapon is the rapier at 1d8, so it's no slouch (equal to a longsword) but it lacks versatility. But you've been watching LOTR, so you want fighting knives (short swords, really), I know.
Before you go all DEX consider the benefits of Strength to the fighter. You can wear heavier armor, which will cap your DEX for AC bonus but not for attack and damage. In this way you can have a decent Dexterity score (15 base) and a solid Strength score (16, maybe). You can carry a longbow and a longsword. Go ahead and take the archery style at 1st level for the +2 bonus to attack, use your Dex for its damage bonus and when that slavering beastie charges to close the gap, drop your bow and use your sword and board, or choke up on the longsword with both hands (versatile property) for 1d10 damage.
At level 3 when you get your Martial Archetype take Champion. As you level Champion will offer you a second Fighting Style spec (level 10) and since you can't take the same one twice you can choose something like Two Weapon Fighting and do your two-blade thing. Or take Defense to get that +1 AC bonus. The point is to be versatile and survive to get those levels and that loot.
Often in fantasy films and films that purport to be historical the bow is a weapon for the slight of build, the squirrely little guys and the girls. In fact a longbow is a serious weapon system that takes years of training to master and it builds a certain strength. It needs a strong pull to be effective and the training is as much about developing endurance as it is about hitting targets for exhaustion is the foe of the archer.
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Just some thoughts. Enjoy your game.