You could watch nodame cantabile. It's quite a cute and funny romance comedy. You can find a sypnosis about the story here
http://www.animenewsnetwork.com/ency...me.php?id=7010
Another anime that is fairly good is Ah! My Goddess. I think it would fufill all your requirements to which path you are going to take.
Fruits Basket is another anime that is kinda sweet but it has a little bit of magic since some of the main characters can turn into animals(Sorry).