Well, everyone here has good suggestions, I would personally start with Death note, and then go on to the other recommended series. However, one thing you should know is that anime has a lot of genres and themes to pick from. Once you get into watching anime, you might find that a particular style/genre/theme might appeal to you. Just pick out any series you're curious about and watch it. Who knows, you might hate it, you might like it. You might even become an "Otaku" in the end. Oh, and you'll find out what that means later on if you don't already know...