My suggestion would be with Full Metal Alchemist: Brotherhood its one of the most recommend Anime series as it is one of the best Anime that is adventure and tugs at some heartstrings.
Or my personal suggestion is to watch the Western cartoon show Avatar: The Last Airbender and then its spinoff The Legend of Korra. They are both like Anime but are far more creative in character development and story then most Anime.
Also, word to the wise, start watching Anime that have relatively fewer episodes as Anime series that have over 100 episodes tend to have Filler episodes. Beware of Anime that continually tend to rely on Fan Service (shots of peoples underwear, stuff like that).
And when your ready, watch Attack on Titan
Full Metal is a good suggestion. There's two versions, so watch the original first, then the second.
Avatar is good if you want little kid adventures. If the airbender one had been on a better network, there could have been more violence and adult content instead of whimsey, which isn't bad in its own way. The Korra one felt like it was written by a fan girl on Tumbler, though.
Attack on Titan is like a starter anime. Ditto with Naruto and Sword Art. If you can watch those, move on to better ones.
Alice, look up Magi and Fairy Tale. I think they're a step above the ones mentioned above and fall in line with what you want. I'm not a huge fan of either, but I think you'd enjoy them.
After that, look up Berserk. And after that, Tokyo Ghoul should have Blu-rays out in all its uncensored goodness.