Git is your best choice, since it allows "cheap" commits, branches, etc. every commit is simply a diff of the previous commit, so the size is minimal, for example if you have
and you only change index.html, then that is all that is stored in the commit, making git extremely space efficient, whats more, it only stores the one or two lines you changed, it could be 500000 line html file (WoAH) making it super fast.
This does mean that the first push to whatever git server that you're using might be long. But everything after that should take no time at all.
And the beautiful thing is, everything can be done locally, you can do as many changes as you want to a local repository, commit as many times as you want, and then push all at once, and since repositories can be local, you can push to just another physical (in the virtual sense :P) on your hard drive, or to a webserver, or through email even!