If you have access to ssh you have several ways to do this, but since you say you have access via ftp, you can access from most modern browsers, just put ftp in the browser address bar, for example:
ftp://meuftp.com.br/
You can still use Fireftp to, then yes, manage a ftp via Firefox , or the sFTP through Chrome .
You also have the option to use a desktop FTP program, there are several, I will indicate the Filizila because it is easy to use and is multiplatform .
Edited | Device Sharing:
A good alternative to backup is crashplan, you install on your devices and they all share the files that you determine, of course you need to be able to install to a provider if you want the files to be stored in your discs.
CLICK TO DOWNLOAD CRASHPLAN.