Can I create an option to pay for a product via credit card or choose to submit the form without paying?

To allow for the user to either pay directly in the form or at a later time, it would require setting up any products outside of the payment field.  Options without numeric values can have values assigned.

http://www.jotform.com/help/301-How-to-Assign-Calculation-Value

Then use a calculation field to produce the total:

http://www.jotform.com/help/259-How-to-perform-calculation-in-the-form

Pass that total to the payment field:

https://www.jotform.com/help/275-How-to-Pass-a-Calculation-to-a-Payment-Field

Then show either the calculation field or the payment field, depending on which form of payment was selected.  Here is the resulting form:

https://www.jotform.com/help/120-How-to-Set-up-PayPal-Along-with-Other-Payment-Options