I associate "cute" with behavior usually the adorable and endearing type. It makes me want to get to know her past the physical which I would describe as "hot". A "hot" girl is just genetically gifted woman who on first impression just looks good without really trying. I would associate "sexy" with how a girl carries herself with a sassy attitude and confidence (borderline arrogance). The kind of woman that has almost nothing that fazes her. you don't have to be genetically gifted to be "sexy"but it helps.
If you are looking for a S/O then "cute" is your best bet
If you are looking for comments on how you carry yourself in a secure and confident manner = Sexy if personality>looks and "hot" if looks>personality
cute is like adorable, a word you'd use to describe something that is sweet and harmless. this can be a good thing, but it doesn't necessarily imply any sexual intentions.
pretty is like gorgeous, a word used to describe someones physical attractiveness. this usually means some kind of sexual chemistry, although not always (such as the brush of "you're pretty, but not really my type").
hot and sexy are purely about sexual intentions, not necessarily about relationships - basically a "i want to have sex with you".
Cute would be the woman in my avatar. I prefer cute over any other kind of woman. I would consider Lauren Conrad pretty. Britney Spears in the music video I'm a slave for you would be considered hot. This is sexy: link