Obviously you should encrypt it either during submission, or after before storage.
The current "best accepted" method is RSA-256 encryption. That's what I would suggest, especially with sensitive info like SSN or bank account stuff. Names and addresses aren't technically sensitive as any bloke with a phone book can find you (if your number is listed).
Anyway, you can either encrypt the data using Javascript into RSA-256 or, you can submit the data and let PHP encrypt it for you. If you just google about the subject, you'll find plenty of scripts and tutorials.