tl;dr: use Dropbox
Dropbox is a transparent to access cloud storage provider that can be used to easily sync files across devices, with platform support for Linux, Mac, Windows, iPhone, Android and also a web interface. It is free to use for the basic account which gives you up to 2 gigabytes of storage. Computer versions can be found here: https://www.dropbox.com/desktop
The beauty of using Dropbox is it will transparently (in the app on e.g. your phone) play the mp3 and remember where you have got to next time you access it.
Example steps: