May be CB user lists functionality come in handy?

It sounds like a CB Userlist is what you're wanting. You can create one within CB > List Management.

How can we include an obligatory user group selection in the CB registration?

Let them select a Joomla usergroup to join at registration? This is somewhat doable, but it'll take a new CB select field with the usergroups names added to it as values that you want them to be able to select. Then using CB Auto Actions and its Usergroup action you can give them usergroups based off that field on the after registration trigger. We've a tutorial for this exact usage, which you can find below.

www.joomlapolis.com/support/tutorials/107-use-cases/18237-assigning-usergroup-based-on-cb-field-value

And once we do and then create a user list, will the user list items contain users with there corresponding groups or not?

You don't need to create the userlists dynamically. Just setup all your userlists in advance within CB > List Management. You select what usergroups this list should display or you can use a CB field to filter the list down to more specific users. When the a user registers and they belong to the userlist that your list is configured to display they'll automatically display. I suggest reviewing your documentation, which you can download in the Advanced downloads section, as it explains userlist usage and more in great detail.