The following are just a few popular solutions available to you depending on whether you need a full eCommerce website or just subsections where payment will be required. If your are selling goods and your shop is in the United States, then you will probably need a system that supports shipping modules, calculates state and local taxes and is secured (https) with a secure certificate.
Magento is an open-source content management system which was developed exclusively as an eCommerce solution. The community edition is free to download and use. With the community edition support is via forum. The enterprise edition is built for larger shops and has a richer assortment of fetures.
Zen Cart® is a full-bodied, user-friendly, open source e-commerce product. The ZeCart team says, "The ecommerce web site design program is developed by a group of like-minded shop owners, programmers, designers, and consultants that think ecommerce web design could be, and should be, done differently. It is PHP-based, using a MySQL database and HTML components. It branched from osCommerce as a separate project in 2003. Support is provided though an extremely responsive forum.
VirtueMart (formerly known as mambo-phpShop) is an open source e-commerce solution designed to run within Joomla CMS. The key with Virtuemart is that your website must be Joomla CMS which you install and configure first, then Virtuemart. Besides Joomla there are half a dozen various Joomla eCommerce extensions. Cruise the Joomla extensions directory to find out about some of the others.
PayPal is a service that enables you to pay, send money, and accept payments without revealing your financial details. Most eCommerce solutions can be configured to work with one of the many available PayPal solutions. It is a worldwide solution.
Stripe is a U.S. based company that allows both private individuals and businesses to securely accept payments over the Internet. It was designed for developers as a solution that can be configured to work with a wide variety of payment gateways such as PayPal, Worldpay and Authorize.net.
RSMembership is a Joomla Membership and Subscriptions Manager developed by RS Joomla. As with Virtuemart, your website framework must be Joomla CMS.
Foxycart is what I describe as a semi-hosted solution. You use whatever system you want as a framework for your website. You set up your shop with the Foxycart API and when the customer makes a purchase the product information is passed to the Foxycart hosted backend where checkout occurs.
WooCommerce is an eCommerce plugin that helps you sell product on a WordPress CMS website.
