FTP is a good way to solve your problem, you setup the FTP server (google vsftpd) to listen on the interface and forward your port 21 (20 is wise too) from your router to that machine. Then get a dynamic DNS service like someone mentioned (unless you have a static IP) that will constantly update the domain name they give you (loads of free ones) with your IP address.
Then to see/download your files ftp://usernameassword@
<your IP/Domain>:21 (or use an FTP
I found this brilliant if you listen to usic on loads of machines, is an audio server that streams the songs, easy to setup - http://gnump3d.sourceforge.net/