The default music player tends to look only at the phone's internal storage and SD card for music files.
The default folder for music is "/Music". It only plays the files, no downloading.
If you don't have any MP3 files (or the like) on your phone, there is nothing for the basic music app to play.
Most of the time I convert a bunch of music CDs to MP3 files on my computer then copy them to the phone.
If you want to download the music, most legal sites have their own app.