I suggest WooCommerce, which is a free WordPress plugin and one of the fastest growing shopping carts. Many small business used WooCommerce for their online store. They recognized that it allows them manage site with simplicity and SEO friendly. It is difficult to say that WooCommerce is the best SEO friendly CMS platform. However, I think it is a good solution for small business because of cheap cost and effectiveness.

If you are sure about WooCommerce and WordPress, you should try WooCommerce migration tool by Litextension to convert to new site with keeping SEO URLs. Check it: http://litextension.com/woocommerce-migration-tools.html