Shopping carts
Ecwid by Lightspeed has one of the best full-featured shopping carts designed for easy integration with an existing website. Ecwid hosts the cart, while the web developer need only insert JavaScript tags into an existing site. As an example, I placed the Ecwid code for a sample bike shop in my fitness site, LiftforHealth.com.
There are many open source carts that one can download and then host. These open source sites include CubeCart, PrestaShop and AbanteCart. In some cases, though, the files are absolutely massive. So far, I have found Ecwid to be much easier to use.
Gartner has an overview of the various solutions.
As an experiment, I put together a simple, lightweight (but limited feature) shopping cart. I used jQuery shopping cart code from CodeHim for the basis; upgraded the cart from Bootstrap 3.4.1 to 5.3.3, added a Bootstrap-based carousel, and used the JavaScript fetch function to develop an application program interface between the cart and Stripe.com. As such, the cart can be used to purchase products by taking the buyer to a Stripe.com checkout page. Stripe.com has backend scripts for tracking orders.
The experimental shopping cart can be found here. If the seller only offers a few products and does not need advanced features, such as a customer login, coupons, a rewards program, the experimental cart is fully functional. If advanced features are needed, I would recommend Ecwid, Big Commerce, Shopify, etc.