2-hander weapons are usually for warriors who don't worry about their health bars, and work on the orc mentality that smashy smashy is better because bigger. Classic warriors are, yes, 2-handers or sword+shield users. It really depends if you want to think about your defenses or not.
dual-weilding is more for lighter characters that are more focused on a spinning, kicking whirlwind of death. They do the most damage, by the way - if that is your thing, then go for dual-swords.
Generally, you either choose between axe, mace or sword. Swords get a decent perk for +chance to do critical damage, and they swing pretty well. Maces (and hammers) have perks that bypass armour, which makes them very good against tanked-up enemies. Axes.... Well, they supposedly do bleeding damage, but the guide lists that as being roughly equivalent to weak poison spread over 3-4 seconds... Not worth it.
One thing to note is that if you go with a two-handed weapon, they have significant swinging time. Especially the battlehammers. So you really want a high armour rating, otherwise you will lose too much hp while swinging / recovering from the momentum. Thus, heavy armour would be better. If you go for a shield, then both armour types are viable, imo, but know that your damage will not be high enough...
If you want a nimble powerhouse in light armour, go for dual-weilding offensive. two-handers with light armour don't really go well together; the nimbleness of the armour is negated by swing speed, and you will be lacking armour rating for quite a while.