I would suggest watching anime that a lot of people know to test the waters and see what genres you're into.
A few that I would suggest would include...
Death Note Fairy Tail Ouran High School Host Club Fullmetal Alchemist Vampire Knight Black Butler Soul Eater Sword Art Online Attack on Titan Code Geass The Melancholy of Haruhi Suzumiya DuRaRaRa!!
anda oleh no means have to watch all of these. They're just rather populer anime that most everyone in the anime world knows at least something about.