Can I create a form that will show them a pdf proof after?

I would upload a background template, and then the data collected in the fields of the form would fill in on my template to show a proof.  I basically want my customers to input data for their biz cards and they can see proof before I print.

You can create an email autoresponder and include a PDF report of the submission, this guide will help you configuring the email: https://www.jotform.com/help/26-Setting-up-an-Autoresponder-Email 

However, it's not possible to upload a template for the PDF report, the report can only be customized on our web site as explained on this guide: https://www.jotform.com/help/384-How-to-Customize-PDF-Submissions-Report 

I hope this helps.