[kmg]

Webmail clients don't do mail storage like desktop mail clients like thunderbird/outlook, i.e., there is no "download messages for offline use" option. Some usually cache message data of mails you accessed, but that's different.

Most webmail clients talk to a backend IMAP server which does the storage. The most popular and open format for mail storage is Maildir. So get a local IMAP server running with Maildir and access the IMAP server with http://roundcube.net/

Considering that you have 8GB of mail, I would suggest you go with http://dovecot.org/ and its mdbox storage instead of Maildir, that way if you don't like dovecot for some reason, you can convert from mdbox to Maildir to migrate.

The last piece of the puzzle is to bring in new mails from your mail account(s) to your local IMAP server. For this probably a tool like http://wiki.github.com/jgoerzen/offlineimap/ can be used.