Cute-usually accompanied by a good personality that makes them have a certain glow or appeal that makes you say aww! or just a sweet smile. There is something about cute guys that makes them seem more genuine and heartwarming which goes along with their good looks.
Hot- seriously you just want to jump their bones. more like a sexual attraction to their body/face/image.
Handsome- classically good-looking. can be hot but not usually in the cute category. more about the face and less about the body (but a good body does help). Everything is almost "fairy tale" good looking, as if he could be a model or you could picture him as prince charming.