You can create products in Shopify and use the Shopify Buy Button to add your products to your current website. For each product or collection, you create a buy button with, a code will be generated that you add to the theme of your website in the area that you would like your products to appear. Also, you can use your own domain name with Shopify. If you have an existing domain name, you can connect it to Shopify from your store’s admin. If you don’t have a domain name yet, you can either buy one through Shopify or a third-party provider. I used Magento for similar purposes and it was a great choice. At https://amasty.com/installation-service.html you can find information about the installation service of this great product.