First off, Avatar The Last Airbender is not an anime... that being said GO WATCH IT!
Naruto/Shippuden is good, but you can skip like the last 12 episodes before Shippuden cause the were fillers till the manga had a large enough buffer.
Either Fullmetal Alchemis is worth watching.
Death Note, can get wordy at times and contains the least amount of action. A decent anime I would get around to watching, but I'd put it near the bottom of this list.
Ghost in a Shell, (the movie is worth a watch, a little word and philosophical thought). The to anime series have great action sense, but you'll need to sit though a few episodes of dialog at times to get to them.
Cowboy Bebop, great show, ends a little sad but is a better reflection of real life in that sense.
Akira... DO NOT WATCH... ok let me elaborate, that movie pulls about 80-85% of the story from the first volume and the remaining bits piecemealed from the next five volumes. For the time is was made it was a great display of technical and artist know how, but storyline wise its a monstrosity of a mess. For anyone who is serious about graphic design or animation its worth a viewing or two.
Still haven't gotten around to watch/read Beserk yet.
While its not on your list, Elfen Lied is a great anime to watch. One of the only ones I know that is popular with both my male and female friends.