Do headphones hurt your hearing? which type would be better? thanks

It depends: It depends on how loud you set the headphones and for how long you have been using them. There is no particular type per say that is better than another. It depends on you loud you set them. If they are so loud that you "hear" a ringing after using them. That is an indication of auditory trauma. I would say to set them at a level where you can hear the music, but others around you can't.