It turns out that I cannot use Nullmailer so that Logwatch and other services, like Wordpress, can send email. So I have just now set up Postfix by issuing two first two commands here. I now wonder if there is anything else I need to do post-installation to make sure that Postfix is working properly and is secure.
I've tested to send email through Wordpress and it works.
Note: Postfix will only be used to send outgoing email by the system. User email is managed using Google apps.