Why recreate the tasks available with logrotate? It’s already installed.
Say you’re backing up files something like this:
# tar czf /backups/full.tgz /
Now you can have logrotate manage rotating the old ones out, keeping the new ones in order with a quick config:
# cat /etc/logrotate.d/backups
/backups/full.tgz {
rotate 10
daily
nocompress
notifempty
}
The rest is automatic.