SSH is normally used to access a UNIX shell (like a Windows command prompt, but much more powerful) on a remote computer with every part being secured by encryption. Commercial products and free products like Cygwin allow SSH to work on Windows too. It takes a little getting used to because it acts like UNIX. But once you're used to it you can use it to move files in Windows with relative ease. There's a utility called rsync that was written by the same guy who wrote Samba that's immensely handy for doing incremental backups. The rsync program was designed to use a remote shell program, and as long as you have SSH public/private keys set up (I'll skip this) you can back up your Windows home directory to a Linux machine without using Samba like this:
rsync -rtvzPS /cygdrive/c/Users/myusername linuxbox:/home/myusername/backups/windowsboxname/
The myusername parts may be different on different machines, so you need to adjust that if necessary, as well as the letter after "/cygdrive/", and the path beyond that, depending on your version of Windows and how it's installed. You can use whatever names you like on the Linux box for the destination, as long as your Linux user owns the location and the directory structure exists. Just substitute your path on the Linux box and you're in business.
You can install the sshd program as a Windows service and copy files from the Linux machine's console, and put it on all of your Windows machines. The rsync program does some things that the DOS/Win XCOPY program can't do, which is why I prefer it.
If you want to eliminate Windows altogether, the first thing to do is get used to using `man' and the newer `info' command (also the `--help' switch) to learn more about the bash, ssh and rsync commands in Linux. You can look on the web and use dead trees books too, but IMHO diving into using the UNIX shell straight away is best. The same applies to other command line programs, and most importantly, shell scripting. Just like there are some things in Windows that are just plain easier to do with a batch file, writing your own Linux shell scripts is helpful even when your Linux distro can be controlled through the GUI.