I use the Stiva Shopping Cart solution from PHP Jabbers. This is a totally independent shopping cart that you can integrate into a Blocs-built website. Essentially, the shopping page is created as a separate page in your site which is built automatically from the PHP script. You can top and tail the page with any other blocs or brics and you can also change the appropriate CSS file associated with the script to style it differently from the standard look. It comes with a few preset styling options so you can start using it without modification.
The script has it’s own admin area where you can manage your products, upload images (several images per products), edit descriptions, prices and payment methods. Paypal and Stripe are a couple of the standard payment options, but the developers can integrate other payment options. I suggest you take a look at the demo page to get a feel of how the script works and looks.
You must be running PHP on your server for the cart to work, but once installed, you will not be relying on third party websites to deliver your shop. Installation support is offered at no cost so you don’t have to worry about setting it up correctly on your server.