If you use WordPress you can install a plugin that, when used with a shortcode, would enable an embedded audio player to handle the specified file. So that would take care of playing the file once it was on the website.
Next you would enable posting by Email to that WordPress blog [in the settings somewhere].
In the Email subject write the name of your post. In the Email body you would write the shortcode to enable the audio player & specify the file name & location; finally attach the file to the Email & click send.
It should then show up as a posting, with the mp3 file ready to be played used the embedded audio player.
This isn't the only way to do this I suppose, but this is the first way that came to mind.