WooCommerce is used by many to sell products online. It is easy to use it to build a public store. You have some work to do to manage a private store. Build Private Store For WooCommerce can help. It is a handy plugin that lets you create private products. It has a customizable login and registration title.
With this extension, you can restrict content and product access only to members. You can also restrict access to store products to guest users. Guest users won’t be able to view your protected pages. The premium version of this plugin lets you set a custom user login redirect URL and customize approve/email rejects.