I have searched something like this for backups, but have not found anything good. But I also have conflicting wishes. I want it to store the history (so that

I have searched something like this for backups, but have not found anything good. But I also have conflicting wishes. I want it to store the history (so that a backup of directory A cannot be overridden by a backup of an unrelated directory B, and it can apply renames without copying large files again), and then I do not want it to store a history (so that large files that are removed from the main system can be permanently removed from the backup)