This, as usual, is not the final word, and others may well have differing experiences. Interestingly, the first approach to the classes seems to have assumed that bows would be used for pulling, with shield and 1H skills used in melee. Very very few archers do that, not because it is ineffective, but because players become archers in order to use bows, and keep using them at melee range.
The scout school receives 10 skill/level in Armor Use, Bow, and Crossbow, and 8 per level in evasion, magic defence, One Hand Pierce, Crush and Slash and shield. Strength is 7. Power and Focus receive 5/level, so the class is heavily biased towards the physical. There is no prerequisite. This is the archers' equivalent of warrior, with the ability to upgrade weapons and armor the soonest of the three classes (without using training points.)
Elemental Archers receive 9 points/level in Bow and Crossbow, and 8/level in magic defence, evasion and armor use. Strength is 6. Power is 7, and focus is 6. Armor is limited to ring and chain. Watching elarchers, it seems that they have the strongest offence of the three schools, which is offset by a bit weaker defence. Somewhat like mages in that respect. A friend of mine solo'd the AoP premerge at level 92 or so. The prerequisite is 20 levels of Scout.
Ranger, which I play, is a hybrid class, and has a substantial caster component. It receives 9/level in Bow, Crossbow, Evasion, and Armor Use, 8/level in the 1H skills, shield, and magic defence. Strength is 6. It also receives 7/level in Nature, allowing nature spells to be used without multi-classing. This provides access to stuns and roots, which are very handy. This versatility is obtained at the expense of higher training requirements, as 20 levels of scout and 15 of druid are needed. I preferred taking the scout first, as the 1H and evasion skills are useful for leveling druid. When doing the druid portion, I strongly suggest becoming acquainted with, and comfortable in the use of, the nature spells that are available. You will be much more versatile. I used 1H skills almostexclusively as druid, and that delayedmy education in spells.
With multi-classing, the ranger can use a very wide range of spells. For example, with some cleric/healer, the ranger can cast Gifts, Enhances, and Surges, as well as the Revitalize, Purify, and Resurrection spells.
The ranger is considered a jack-of-all-trades, with no outstanding skills in any one area. I find that the combinations open with multi-classing make the ranger a strong player, in support roles, limited tanking, and soloing. Self-healing in addition to stuns makes soloing more viable than it may first appear, and with suitable multiclassing, casting augmenting spells, heals, wards, and resistances on fellow players (and if all else fails, resurrection) plus pulling capabilities, make the ranger a strong contributor to a group. Limited tanking (remember those evasion training points?) works pretty well in a pinch, although a healer in the groupwould not be a bad idea.
All three classes are limited to ring and chain armor (or soft armor, but there is no point in doing that). And all three have relatively low strength,which affects damage. I (without knowing about this) chose armorer as my craft, and received 9 Str/level, so at 100/100, the armorer has made a substantial improvement in my strength. In round numbers it is 900 instead of the 600 that it would be without armorer. Fitter also provides a lot of strength, 10/level.
As ranger, I did not "unlearn" scout, so have kept the Long Shot ability, which is verypawful (some say "handy") for long distance pulling.
I put a few training points into Bow, so I could use a better bow as soon as I met the level requirement, and a few points into nature so I could use teched nature spells a bit sooner. I put most points into evasion and magic defence.
I will edit this to add information after I have done some further research, to be sure I have current information. The information above is based on the book, and I believe that it is still current.