Building a secure contact form

If you just check to see if they mailed you in the last few minutes and they were "adding" something to the last email then you have a problem they cant re-email you and they might go elsewhere for work.

I would do simply checks making sure email is valid format, take the ip, and add it to the database

On one of my old sites I had in the admin panel a place setup so I can check the emails and reply/delete them.

If they already had sent an "email" to the database just add it to it with a separator and new time in there.