Yes, you would be able to accept credit card payments on your website being hosted on our web servers. We would not be providing you merchant account services, and thus you need to contact companies like PayPal, 2Checkout or Worldpay to set up a merchant account on your website. Having a merchant account will allow you to accept credit card payments online from your website.
You can have a shopping cart set up for your website through your web control panel to start your online shopping store. We provide installation service for leading shopping carts with our web hosting packages. These shopping cart applications are included in Fantastico with our Linux shared hosting packages and need to be installed through Plesk Control Panel for Windows shared Hosting Packages.
We highly recommend you get a Private SSL certificate to start accepting payments via credit cards online. An SSL certificate will ensure secure online transactions and avoidance to any vulnerable attacks.