I have a Mage, and have had her use a steel dagger and sword, improved of course to lift the damage rating a bit. When she fights, I love watching how my char will do a fast spin, cutting her opponent sideways. Or how she'll shove both into a Draugr, one in its throat, the sword in its gullet.
You won't get credit for 2-handed weapon, although I don't know why, as the char is, but whatever. Also, if your sneak is good, you can get right on a Draugr, and have at it before it can get up. I also had her loot a Draugr Bow, improve it, and watch them fly when an arrow hits.
Oh! Btw! Welcome to these Forums. Lots of people here who've been playing for awhile (18 months for me, I had 3-chars at one time for awhile. And I'm able to play Skyrim a good part of the day). When you can, show what platform you play on, each one works differently.
Just remember, it's a game, it's buggy as hell, glitchy (depending on the platform you're on), but it's still a great game. Just have fun with it, and ask if you're not sure. Googling for info will help as well, at times.