I find there is no better way to back up your system than using rsync [...]
I think that using rsync is very dangerous unless you are very much in tune with what you're doing: it does not cover you against one of the most frequent needs for a backup - you create a file, then delete it or overwrite it, all within one of the rotation cycles you mention. rdiff is excellent for some backend tasks, like syncing your proper incremental backup to a remote location. Once you start wrapping rsync with enough stuff to make the backups incremental, you have reinvented other programs like rsnapshot and rdiff-backup. I don't resonate with rsnapshot, although it is a good system. It involves too much central setup. For lightweight programs that you can understand easily I recommend rdiff-backup. I then get fancy by backing up to an encfs area, and then rsync the raw encfs area to remote locations, but you don't need that. Something like this already gets you going, just run it by hand. rdiff-backup --exclude-other-filesystems -v 5 $HOME /media/MY_EXTERNAL_DRIVE_LABEL/backups/home