I'll give you my recommendations, but I should point out that I enjoy anime that are very Japanese. As in shows that are extremely wacky and/or over-the-top ridiculous while simultaneously having hard-hitting melodrama. Looney Tunes combined with Game of Thrones. Here's what I recommend to you.
One Piece - Action-comedy series starring a group of pirates. Think Young Justice, but much, much better. One Piece is currently the most popular manga/anime of all time in Japan. First 4-5 episodes kinda suck.
Gurren Lagaan - Deconstruction of giant robot series (like Neon Genesis Evangelion) with an excellent cast of characters. Fairly short at only 26 episodes.
Code Geass - Military drama set in an alternate present where the world is controlled by three superpowers, The British Empire, The Chinese Federation, and the European Union. The series takes place after Britian conquered Japan and is about the conflicting ideologies of the two main characters. Lelouch, who seeks to overthrow the British Empire, and Suzaku who wants to improve it from the inside. Also, giant robots.
Based upon the length of my summaries, I think you can tell which series I recommend most to you.