"Kind" and "type" are used interchangeably, but we would never say "class" in reference to music. "Class" sounds very scientific or analytical. You will mostly use "kind" and "type."

What 'kind' of music you like implies the person asking wants to know the characteristics or qualities of the kind of music you like. Do you like happy songs? Sad songs? Mellow songs? Acoustic songs? Loud songs?

What 'type' of music implies the genre of the music. Do you like rap? Pop? Hip hop? RnB?

These are subtle differences and 'kind' and 'type' are often used interchangeably so don't trouble yourself too much trying to remember the difference. Don't use what 'class' of music do you like because that is never used.