Cute is childish, normally used for kids and guys a girl find attractive but aren't really interested in. Sexy is sexual, normally if a girl calls a guy sexy they are only interested in the guy's body. Handsome is more polite and usually means the girl likes everything about him. Being called handsome is a good thing.
Out of all, I'd say handsome is best. When I think of cute, I think of a kind of young, guy who has soft features. Hot you have is kind of a sexual thing, where the features are more harsh. But handsome. Handsome is best. You have stronger features, and it seems more mature manly. Cute and hot will fade but handsome lasts forever.
This is the though process of someone wanting to compliment you- "If I call him hot, it seems like he's just a good looking person with nothing else to compliment on. If I call him cute, he might think that I'm downplaying the way he looks and sort of treating him like a baby...I'll call him handsome because he has class, he's good looking, and he acts like a gentleman."
It is a much better compliment than just cute or sexy. I was pretty excited once when I was a kid and someone called me 'charming'. I felt like a natural born lady killer :)