It has been awhile, since I moved a config database, so I will defer on this one.
However, you are right on the money for content databases. I perform a sql server backup to a *.bak file. I move the *.bak file to the new server. I restore the *.bak file as a new database. I go into sharepoint central administration add the content database. ( Central Administration > Configure Virtual Server Settings > click on Web Site > Manage Content Databases > Add Content Database > Specify database server settings > Enter database server name & datbase name).
If you are simply moving the sql server database, for performance, failover, space reasons to a cluster. Then I would move the content database first before the config database. I would remove the content database from the existing environment within central administration. Then I would perform the backup and restore as listed above. Once you have confirmned that the new database on the new environment is working well. I would delete all traces of the content database on the local server.