Should my character use two-handed weapons or a shield and one-handed weapons. What are the benefits of using either one?

2-handed why you might ask well..... Conan uses two-handed weapons.

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anotherdaedra2 is right. Only sissies use shields. Strap a shield onto your arm a shield the next thing you know you'll be carrying a purse. No, any self-respecting Barbarian is going to wield a 2-handed weapon. The bigger the better. If the weapon is even larger than the Barbarian him (or her) self, why so much the better. Crom does not favor the weak.