As with all things, there are many sides to anime. There is a raunchy, disturbing side to anime, but you don't have to concern yourself with that. Death note is a great one. Also, try Full Metal Alchemist. There are two versions, the first one deviates from the original manga and is less serious at times, the other version, Full Metal Alchemist: Brotherhood, follows the manga almost exactly and is stays serious the whole time. Both are fantastic with awesome stories. Angel beats is another great one. It's more whimsical than Full Metal Alchemist or death note, but has a very fun and deep story. I shed a manly tear at the end of that one. Huge plot twist at the end. Those are my suggestions! Go!