Sync multiple computers to a central server

[Derek Maciel]

I'm a high school freshman, and I edit scripts and such from my school
computers (which may or may not be the same computer every time), and
my home computer. All the files will be hosted on my server, and I'm
trying to find the best method to synchronize these computers using
minimal bandwidth.

The computers that are involved are:
 * My home computer, which runs Windows 7
 * My school computers, which run Windows 7 and Windows XP
 * My server, which runs Ubuntu 10.04LTS Minimal

About half of the files I work with are hosted on my server's git
repositories, but not all of them are.

The method I've developed so far is:

On home computer:
 * If files exist, delete them
 * Download up-to-date files from server
 * Edit file, save.
 * Upload to my server
On other computer
 * If files exist, delete them
 * Download up-to-date files from server
 * Edit, save
 * Upload to server

As you can see, any time I would need to edit a file, I would first
need to delete it (as I cannot remember every time if I have edited a
file since the last time I have downloaded the latest version on this
machine), and then download the latest version.

If it would help, I could build a server in my home that could serve
as the central backup spot, and have all the other computers sync with
my home backup server, then have my production server sync with that
on a cron.

So, does anyone have any suggestions for how to synchronize these
files optimally? I was going to use rsync but it's a little tough on a
school computer: I could install software if needed, but it can't
interfere with anything anyone else would do on the computer (since
other people would be using them).