How do I select the users who can register?
By that are you implying that some users will not be allowed to register? OpenID only provides minimal help there. If the users who are allowed to register happen to correlate to the users who are members of certain OpenID Providers (like Google and Yahoo) you can filter the allowed OP Endpoints to those "white-listed" endpoints. Otherwise you can send the user through your own custom selection criteria by asking them your filtering questions after they log in but before they are allowed to proceed further in your site.
I also need some billing information and credit card number. How can I relate this information with that provided by OpenID? Do I use my own users database?
Yes, you must have your own users table -- just without username+password columns. You won't get any billing information via OpenID (yet). You'll have to collect that yourself. You associate the data you collect with the user account you created when they logged in. OpenID offers a "claimed identifier" that is the functional equivalent of your user primary key, although DBA-wise you should just use an INT as your primary key and add a unique constraint on the ClaimedIdentifier column.