Welcome to Android Central! The best place to copy music files to is the Music directory on the phone's Internal Storage. If the music files are of a compatible format, then they will get added automatically to the phone's music database.
Where are the music files coming from? Be aware that music purchased from Google Play Store gets added to your Google Play Music library in the cloud. If you download the music using the Google Play Music app on your phone, the songs are for offline use by that app only -- you can't manipulate those files or play them with a 3rd party music app. In order to do that, you'd have to download the music from the Google Play Music desktop site, from My Library. Then transfer those mp3 files to the phone's Music directory via USB connection.