Barbarian gear is mostly pretty simple—A big bag full of weapons, and a few potions in case things go wrong.
As a result, many barbarians ignore armor class and pick their armor based on its secondary effects. Fearsome armor is a common choice, as it will help keep secondary mobs off you while you are pounding on your chosen target. Light or Medium armor with greater elemental resistances or other desirable effects like fortification or deathblock is also recommended.
Adamantine or any other armor with damage reduction would not be a good choice as it does not stack with the innate Barbarian damage reduction, though it can be helpful if the damage reduction is higher than the barbarian's innate damage reduction. It is highly recommended to wear medium armor, especially at mid to high levels in order to benefit from Physical Resistance Rating, which can help mitigate melee damage received.
Barbarians are typically either 2-Handed or 2-Weapon fighters, and so rarely use a shield. DR Tanks would be the exception.
Based on your fighting style, it is recommended to carry a large variety of two-handed weapons (Or two-weapons that you are proficient with) that have a variety of useful damage modifiers. The only limitation is your inventory space, not your weight capacity. Holy of Pure Good is one good example of a weapon that deals ideal damage. You may also carry specific weapons, such as greater bane weapons, or even weapons that have a vorpal-like effect on specific creatures at higher levels. At higher levels, the capabilities of weapons are such that other effects added may be enough to outdps greater bane weapons, even if the monster itself cannot be killed outright on a confirmed roll of 20.
Greatswords and Greataxes tend to be the most common weapons seen with a barbarian. Falchions can be used, though uncommon to see due to its lower base damage compared to other two-handed weapons, though it does have a higher crit rate. For two weapons, Khopeshes are recommended due to its balance between good base damage and good critical chance/damage. Bastard swords may also be used, typically dealing slightly more base damage than a Khopesh but less damage and chance of a critical hit.
Fortification Item - Heavy fortification is preferred, but even moderate fortification is better than nothing. At higher levels, it is recommended to wear an item with 25% or more exceptional fortification in addition to a heavy fortification item to help reduce the chance of sneak attack and critical hits by enemies capable of bypassing fortification. Even 10% is enough to make a difference, however.
Featherfall Item - Standard item for all classes.
Underwater Action Item - Useful for all classes.
Jump Skill Item - Rarely needed on a barbarian since their strength lets them jump pretty well anyways, but sometimes a bit extra helps.
Balance Skill Item - Some DDO mobs love to trip, and you can't do anything while you're on your back. These aren't necessary all the time, but should be worn when facing mobs that trip.
False Life Item - Again, more hit points are always good.
Potions - Remove Blindness and Remove Disease just in case you get hit with something and the cleric can't get to you immediately. Lesser Restoration is something you should carry in bulk since it can not only get rid of several unwanted effects, but also gets rid of the fatigue after your rage ends (a clicky will work for the post-rage blahs, but pots are needed if you get hit by something while raging). And, you should also carry a large stack of healing potions since they are your only method of self healing.
Augments A named item with Augment Slots are a great way to add more versatility to your barbarian. At level 8, a sapphire of heavy augmentation is an excellent way to mitigate damage at low levels, and can be used until an item with heavy fortification can be found. Augments that boost your physical resistance rating are recommended at all levels, especially higher levels, to help reduce incoming damage. Additionally, you may mix and match the augment effects listed on the augment slot page to add effects you normally may not have, such as deathblock, feather falling, underwater action, exc. It is recommended to find at least one item with 2 augment slots, with at least one of them capable of holding sapphire augments.