I would suggest watching 아니메 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!!
당신 의해 no means have to watch all of these. They're just rather 인기 아니메 that most everyone in the 아니메 world knows at least something about.