You would need both secure web service and a PGP/GPG. The secure web service is needed to secure the connection to the web browser. PGP/GPG is needed to encrypt the information in the e-mail message. An e-mail client that can decrypt the message will also be needed.
DreamHost makes it easy to set up the secure web server - in the web panel for "Manage Domains" just click on the "Edit" button in the "Secure Service" column for the appropiate domain. DreamHost does all the configuration for you.
Encrypting the e-mail message is the hard part because you have to set that up yourself with a bit of a learning curve if you're new to PKI.
In my Perl scripts I use the gpg program (Gnu Privacy Guard) to encrypt the message body before piping it to Postfix sendmail. For this to work, I have a GPG user for both the web site and the recipient. The script encrypts the message for the recipient, and the recipient uses a custom install of Squirrelmail with a GPG plugin in order to read the messages - from the secure web server of course. Personally I use the Mozilla Thunderbird client and the Enigmail plugin.
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