Hi,
From what I understand, you want to create a custom field of the table "user" via the menu Display>Custom fields, so that the customer can select it during the registration, and configure the setting "User group on registration" of the HikaShop configuration to set the group of the user to the one selected in the custom field.
Then, you can restrict the products to the user groups you want with the "access level" setting of the products so the logged in users ill only see and have access to the products restricted to at least one user group of their user account.
Doing all this will require the Business edition, but yes, it's possible with HikaShop.