I would like to create an Archer. Should I pick a Ranger or a Fighter?

First of all, building a character that cannot do anything other than ranged attack is a bad idea. In terms of DPS, ranged attack in DDO is really inferior option compared to straight melee style. If you are new to the game, try straight up melee characters first for the better understanding of the game.

So, fighter or ranger? Originally this question came down to whether you wanted to specialize in pure damage or wanted good variety in skills and spells.

In DDO though, not only are composite bows made for higher strength bonuses not available, rangers at first level get the Bow Strength class feat which adds their Str bonus to bows.

The current mainstream argument seems to be if you should pick a ranger for the powerful capstone enhancement (25% ranged attack speed) or a mildly multi-classed fighter such as a Rng2/Ftr18 to still give yourself access to all the feats of the fighter, including the important weapon specialization, while still getting the Str damage bonus.

Compared to a fighter, the ranger can have a better dexterity, as his class enhancement is for +3 Dex. Level 9 rangers also get the Evasion feat, which makes your high Dex even more useful. Due to the lack of Power Attack or melee for fighting two-handed, an archer will not have too much problem in hitting his target, so strength can be more important than dexterity (at least in the upper levels).

You can benefit most from the free feats of the ranger if you take two levels of ranger and 18 levels fighter. The second ranger-level will give you +1 dex (through enhancement) and rapid shot (1 level for 1 feat in contrast to 2 levels for 1 feat as a fighter).

The fighter is the most versatile damage-dealer of the game; there are many feats which support ranged attacks you won't ever get as a ranger.