If you're looking for a cute romantic comedy, I definitely recommend Ouran High School Host Club. It's really goofy and cute, and doesn't go too overboard with the romance. Plus, I hear that there's a second season on the way.
The first anime I watched was Sword Art Online and I think it was a good one to begin with. It's english subbed so you have to pay attention, but it was really good, especially if you're into video games. Unfortunately that's the only one I actually really got into, so that's all I can say. xD