Ignoring the whole debate about whether to include system files in your backup, rdiff-backup sounds a lot like what you want. It stores your latest backup as plain files on-disk just like rsync, checks the box for incremental backups (older versions of files are stored as diffs, which you can easily browse with rdiff-backup-fs) and isn’t much different to use than rsync. That said, people will point out that you can make rsync do pretty much the same stuff using hard linking.