For me cute and good looking are interchangeable, but cute can also be an innocent look. good looking means you're attractive at least. Hot can mean really attractive. and handsome is like the guy has really good facial features and looks suave or something.
Cute to me is young looking HANDSOME is different - like has good features could be a model type - polished well groomed - well dressed -- and we manicured - my boyfriend is handsome to me - I would a handsome guy... Oh and HOT -- is like the biker boys that are buff, sexy - have the tough guy exterior... I like hot boyz too - but that does not necessarily last I think handsome men grown older to be even BETTER looking as they age.