I see that for many larger projects, people usually choose Magento with customization (for PHP website) and Nopcommerce (for .NET website). Both are open source and I think they can customize many things on it.
I have some choices for you. Wordpress WooCommerce, BigCommerce, Shopify, Prestashop and Magento seem to be prferred by almost people. However, Magento is more suitable with big site because it costs quite high price and require technical skills. You said that you plan to open a small web, so you should concern the rest.