Hi,
Yes, the payments will be secure as the payment itself will actually happen on PayPal (you'll see that you'll get redirected to a payment page on paypal.com at the end of the checkout where you'll be able to pey either with a PayPal account or a credit card, and once done, you'll get redirected back to the shop).
So no worries regarding the security. Having a SSL certificate is nice, but it's not mandatory to accept payment securely. However, if will help for your credibility towards your customers and improve your SEO so I highly recommend you to have one. If you have one with Let's encrypt, then you should be fine.