How are weapons broken into the new Weapon types?

So, I've always been a Sword-user. I just like how they look, and there are quite a lot of awesome-looking swords. With the new weapon-system, though, it seems kind of all over the place. I've seen Unarmed weapons in all three types (Finesse, Light, and Heavy), and Swords of at least two (2handed notwithstanding). It's sort of confusing, and I'm trying to decipher how weapons are put into these different classifications, and which weapon-type is going to be the one that fits me best. Anyone care to spread some knowledge? :D