US Copyright law states that the owner or operator of the establishment where the music is being played is responsible for obtaining the required authorization. The compensation you provide to a performer such as a DJ or band does not relieve you of this obligation.
When you purchase a record, tape, compact disc, DVD or similar product you are granted the authorization for a non-public performance, such as in your home or car. There is no public performance right attached to the sale of these products and if you decide to play this music in your establishment you are required to obtain authorization from the copyright owner or their representative.