Hi there,
Firstly, I am sorry to have to ask this question, but I have failed to find a definitive answer.

I have a VPS running 12.04 LTS SE, Apache, and iRedMail for email (Postfix, Dovecot, Fail2Ban and Roundcube)

I am yet to run apt-get upgrade as I am scared of potentially bringing down the whole system.

Obviously nothing is full proof, but for a web/mail server, is the safest process "sudo apt-get update" then "sudo apt-get upgrade"?

Obviously I would first run a complete backup of everything before hand anyway.
Thanks