Accept credit cards online with the Paypal Payflow Pro (Paypal Advanced). Payflow handles all major credit cards.
Customer will not leave your site. Customer will be asked to enter his credit card details in your site and the card details will be sent to the paypal in the background (using cURL) and the results will be displayed immediately.
IMPORTANT NOTE: Your site should use SSL (https) as per the PCI DSS guidelines. J2Store and the plugin depend on the Joomla for rendering the url. Read these two guides to enable SSL in your site.