Take a screenshot of the Security Settings page from the Settings menu so these values can be added on the new server.
Perform a clean installation of RSC (Remote Support Center) on the new server.
Manually re-enter the IP filters and RSC Administrators from the above step.
There is no need to backup and restore the database due to the fact that the SQL connection string is hard coded within the application. Also, the Remote Support Center client will have to be re-deployed to each workstation in any case.