Starting a Barbarian

Contrary to some books, the most important ability for a barbarian is strength, followed by dexerity and constitution. Barbarians will recieve constitution enhancements as they level up, so they can actually start with less con than dex, and raise it later. The dexterity is needed because they wear lighter armor than a fighter or paladin (and the Uncanny Dodge feats at later levels allow dex AC to protect from rear attacks as well). With medium armor, the max dex bonus is 3, so dex 16 is all you need (mithral armor increases the bonus, though)

A typical barbarian will begin with str 16-18, dex 14-16, and con 13-15. Plan to raise strength at levels 4 and 8, and to have the Barbarian's Constitution III enhancement at level 8, for +2 / +3 respectively.

Note that charisma might also be useful for a barbarian, to help with the Intimidate skill (which is a class skill). Intimidate causes monsters to attack you, rather like a "taunt" aggro skill in other MMORPGs. (However, unintelligent monsters are immune to the effect). Plus, barbarians can take an enhancement so that inimidated enemies are Shaken, penalizing their actions. The intimidate code in DDO is still being tweaked, so it remains to be seen how useful it will be.

Although it may be tempting for a barbarian to learn two-handed fighting, cleave, or whirlwind attack, those feats seem less useful against DDO-style encounters than they do in a PnP game. DDO allows MMORPG-style "mob pulling", so it is more likely that your party will gang up on strong enemies, rather than you being surrounded by weak foes. Improved Trip might be better, as you can knock down hill giants one at a time, and then Power Attack to finish them off.

Barbarians get swim as a class skill, but investing any points in swim is discouraged. By level 3 you will probably find a water-action item, enabling infinite swimming at the cost of one inventory space. Jump, however, can be useful both for crossing difficult pits, and leaping over monsters if you get surrounded. Listen is also a class skill, which currently has very little use.

Races
Elves are usually avoided for the constitution penalty, but they can make up for it with the dex bonus at point buy.

Humans extra starting feat is always helpful. They also get an additional skill point to spend at each level.

Dwarves are of course good due to their extra balance and strength. Their penalty in Charisma has very little effect upon a barbarian because barbs usually leave their Cha modifier at base level to start.

Halflings are surprisingly effective as barbarians, because DDO is missing the PnP rule prohibiting small creatures from wielding large weapons- thus a halfling barbarian can swing a two-handed battleaxe as well as anyone else. (The -2 strength penalty for halflings is noticable, but partly offset because of their +1 size bonus on attack rolls, and +2 dexterity bonus)

Warforged barbarians are rather popular (and even featured in the intro movie for the class), but be wary: having more hitpoints than anyone else can also mean you'll need more healing than anyone else. Don't forget that you only get 1/2 the hitpoints back when healed by a cleric. (You might hope stacking barbarian DR ontop of warforge-only DR feats would prevent you from taking damage in the first place, but it won't stop NPCs from chain-casting Magic Missile and Searing Light)