Depends on the Weapon Skill. Favorite Sword is Windshear, because it staggers without Power Attacking, and isn't technically Enchanted, so you can use it with Elemental Fury, or upgrade it even further. Also, Steel Smithing. Not unique, you can pick up a stack of them, but my favorite swords are the Drainhearts, because you can keep Power Attacking indefinitely...
Favorite Bow is the Bound one, otherwise the Gauldur Blackbow, or a Drainspell for anti-mage.
2H, the Blooskal Blade, hands down. In vanilla, the Drainblood Axe, not counting personally crafted ones. If I'm enchanting, I usually start with the Longhammer, or Headman's Axe. Volendrung is always a good choice until you can make better.