The music was created by someone else and is governed by their copyright rights. When you purchased your albums, CDs, etc., you don't own the rights to the music. You are given a limited license to use and copy the music for your personal enjoyment. Not to share with others (although we know this happens), and CERTAINLY not to sell and make a profit from.
The appropriate way to handle this is to obtain a license concerning each song you want to use. Chances are you'll have to pay a royalty for the use of the songs, which could be a percentage of each CD compilation you sell. You can run into serious trouble in this area, especially if large music companies are in charge of monitoring the misuse of the rights, because they'll have the war chest to drag you through the courts. Speak to a music copyright lawyer about the best way to go about this.
Nina L. Kaufman, Esq. is an award-winning New York City attorney, edutainer and author. Under her Ask The Business Lawyer brand, she reaches thousands of entrepreneurs and small business owners with her legal services, professional speaking, information products, and LexAppeal weekly ezine. She also writes the Making It Legal blog.