Would I be in legal trouble if I was to charge others to back up their data with me?

I recently had the idea of starting a Data Backup service in my high school as a student. Each person''s data would be kept on a separate thumb drive, and would not be entered into any computer other than that which is transferring the files. I already have a group of students who would be interested, but I wanted to know if certain aspects, like backing up music, would fall under copyright infringement, or if it would introduce other legal matters.