first. make sure the from name and from email are not the name and email of the person filling in the form. The reason is that your server is sending the email. if the email is then saying its from the email address of the person filling in the form, it may be rejected by the receiving server. this is because an email coming from [email protected] being sent by a server for mycoolsite.com will look very suspicious. so spam blockers will probably kill it.
You should have the from email like [email protected] and use the senders email as the reply-to. this is so the sending email domain matches your sites and will be more likely be accepted. the reply-to field means clicking reply will use this address rather than the sender, so your workflow is unchanged.