It all depends on how you're playing the character. Personally, I prefer swords, this may sound crazy, but they feel more comfortable. I feel like they require the least amount of effort to swing, which in turn means I can get more hits in. War axes do more damage, but I just find them awkward. In reality, it all depends on your personal preference. Try them all out, and see what you prefer.
Of course, you always have the option of using a different weapon for a different situation. The nice thing about this game, you aren't limited to only one or two weapons. Start with one, and if you feel like it's not doing what you want, you can always go into your inventory and switch weapons.
As for better overall weapons, again, that's not a question I can answer for you, it's something you're going to have to find out for yourself based on your personal play style and your character build. My fave is one I made myself, a glass sword with a fire enchantment that I aptly named 2Hot4U
Is it the best in the game, hell no, but it's never let me down I'm kinda sentimentally attached to it.