Multiple web migration

We are a promotional gifts company working online that needs a web solution for our multiple stores. We have thought of a solution like Shopify but we want to know if this option (or others) are suitable for our needs which are detailed below. There is a main domain [login to view URL] that will include the entire product catalog and seven secondary domains specialized in more specific products. Secondary domains will correspond to categories of the main domain. E.G.: in [login to view URL] there are four categories (key chains, shirts, bags and others). By entering the main page you can browse these categories without leaving the main domain, in addition, for the categories of keychains and shirts we have two differentiated domains ([login to view URL] and [login to view URL]) these two domains contain the same products that live in the corresponding categories of the main page (but always within their own domain). The templates for all the pages can be the same or similar (variations in colors, styles, etc ...) but we must have the ability to apply different logos to each page. To manage the stores we want to have the same backend for all of them, that of the main page. All the orders of all the pages have to get there, all the user registrations have to be in the database of the main page, etc ... We would like to forget about third-party management programs and be able to take all the billing from the page itself, thus avoiding more expenses and duplication of databases. Regarding the purchase of products, we sell customized products in large quantities. The products will have variations and we need a flexible solution for each type of product. Ex: On shirts, once the reference is selected, the customer should indicate at least four variations (color, size, quantity and number of printing inks) before adding the product to the cart. It is important that you can add 10 units of "red" color and "S" size + 5 units of "red" color and "M" size + 15 units of "green" color and "L" size, etc ... and add them to make the total count. Our pages have been active for many years, so we have a large catalog of products that we would like to migrate automatically from Woocommerce. These are the basic characteristics that the project should have, for questions or clarifications I can answer questions and provide links to our pages so you can see how they work at this moment. P.S.: estimated budget will be considered after clarifying the work to do.