Only post music that you have permission to distribute. ie, music that you have gotten written consent from the band or music labels, music that you have created, or music that is public domain or is licensed to allow for public distribution.

There are plenty of sites that offer music that the artist allow one to legally share out there. Majority of it being from indie or lesser known artists. Most big label music however doesn't. You can also embed music from places like youtube that allow one to stream their videos, however they follow the same logic and will remove the videos on their end if they infringe on copyright which of course would make them not show up on your site if directly embedded.