Backing up postfix + dovecot-Collection of common programming errors

I am renting a single server, on which I installed ubuntu 12.04, postfix and dovecot (and ISPConfig).

I would like to backup the full postfix+dovecot configuration, in order to restore it in case of a HDD crash.

I will need to restore all the imap mailboxes (users names, passwords, etc.) as well as the mails and the folders.

In short, someone with a mail account on the server should not be able to see there was a server crash, unless he/she tried to connect to the server during the short period of time during which it was under maintenance.

My question is:

Which files should I backup ? Ideally, I should backup some configuration files each time I create or delete mailboxes, and other files (that contain the mails) very frequently.

I have already found that I should backup /var/vmail, but I don’t know if that’s enough. Also, should I stop postfix before backing up ? If so, will the mail still be delivered ?