That setup should be fine. The router will act as the computer attached to the modem to keep the signal alive and grab whatever public IP your provider gives you, and then all the computers and other devices will be assigned a private ip and work the same as they do now.

The laptop will be useful for connecting into the router via ethernet if wireless setup is needed, and can't be done wirelessly. Some base stations (like the Apple Airports) do allow setup even from scratch over wireless, but others may not.