Christiaan,
A friend of mine likes to ask people “What are you trying to accomplish?”
If you want to keep the end user’s contact data reasonably private, then the form submission should via SSL should protect the data in transit when sent back to your web server. That should cover the HTTP/HTTPS portion.
Dunno about the phishing part; unless your web page is trying to look like someone else’s then I think you’ll be fine there.
For the e-mail portion, you’d need to make sure that your mail system defers to SSL/TLS and that the receiver mail server does too. Ask your host company about that. If they say something along the lines of “Postfix/Sendmail… STARTTLS is supported… client and server side…” then you’re probably good for that one hop. Subsequent SMTP hops, maybe not but that would be out of your control.
If they reply back with “Huh?” then you might want to look into PGP’ing your e-mail. That’s a loooong conversation about private/public encryption keys and you may be best served by just worrying about the HTTP/HTTPS portion ??