If I have my submission payment through PayPal does that count as my 3 payments for the free option?

Do I still need to purchase an account if I am using PayPal?

Yes, for the free user, you can receive up to 3 payment submissions per month. We reset the counter back to 0 every 1st day of the month. 

If you think the 3 payment submissions per month is not enough, I recommend upgrading your account. Here's a guide:

https://www.jotform.com/help/331-How-to-Upgrade-My-Account