Use rules to automagically send inbox mail to a folder
Use the archive feature in the mailbox cleanup to move mail to the archive. I use an archive for each year.
Sort by names. Any one that you just need their contact info, drag the email to the contact folder. It will automatically move the entire email to the notes section of a contact record. The email will be automatically save. You can go back to the view and delete all of the emails from the person now that you have a contact record.
Use the find button in mailbox clean up to locate files with attachments. You can move them to your own PST file taking it out of the inbox folder which is where your quota is set.