You’re practically asking how to build a custom post type and all related templates, specifically made for your needs. You will not get am answer here, unless you break it up in specific questions. But here are some guidelines:
I would go with WooCommerce and add some CSS to hide unneeded areas in the product edit screen. This way, if your client does need to sell at some point, you’re good to go.
If not, what you need to do is:
- Create a new post type
- Create the archive template for the custom post type with if functions to distinguish between taxonomies with subcategories and taxonomies that show products.
- Use template parts so that you don’t have all scenarios in the same php file.
- Create the loops for these template parts, depending on your needs. Add your JS to filter items dynamically where yo need to and so on.