If you want an e-commerce enabled website, you have a choice of many platforms to build the site on. There are many free solutions available, as well as some which require a monthly subscription.
Woocommerce is our preferred platform for developing powerful e-commerce sites. Being a WordPress plugin, you benefit from all the superb functionality WordPress offers you, on top of the e-commerce features Woocommerce provides.
Being open-souce and based on PHP and MySQL, Woocommerce is free to download and use. You may need to purchase some plugins to expand its functionality, such as integration with a payment provider like Sagepay or Worldpay.
OpenCart is another open-source solution, based on PHP and MySQL. Again there are a host of extensions and plugins available (some free) which extend the functionality of the application. Perhaps not as flexible as WordPress/Woocommerce, it still offers a host of features.
Shopify requires a monthly subscription to run your store, and it hosts your site for you. There are a range of apps available to extend the features available. You can choose from a range of templates, or can have a custom theme built by a developer.