How can I set up a payment option to pay through PayPal or recieve an invoice?

I have a registration form for a golf tournament.  I would like to give participants the option to pay via PayPal at the time of submitting the form or check a box to receive an invoice and mail a check.  How can I set this up so the registration will still be submitted if the participant is not paying via PayPal?

To achieve that you would need to set your products options outside of Paypal payment field. Than you can add one more field to your form where you would ask user if they want to pay by PayPal or by check. Then set condition to show PayPal field if Paypal option is selected. In case that PayPal option is selected you users will be redirected to Paypal page and if check option is selected that will be redirected to Thank You page. More about conditional logic you can find inside of this guide: https://www.jotform.com/help/57-Smart-Forms-Using-Conditional-Logic 

You would also need to assign values to your new product field, in your case check box field and to pass calculation to payment field. 

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

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

https://www.jotform.com/help/275-How-to-pass-a-calculation-to-a-payment-field 

Inside of this guide you can also find how to set up Paypal along with other payment options:

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

Hope this will help. Let us know if you need further assistance.