Deployment Manager works with NuGet packages. NuGet package(s) for the project are added as steps and you deploy the same package(s) to different environments. So you can use Deployment Manager to deploy to Staging environment and once you are happy you can deploy that release to production from Deployment Manager.
To get different behaviour for different environments, there are variables in Deployment Manager and as you mentioned there are transformation files. May I ask, why do you need to rename production transformation file to Web.config? Deployment Manager will apply transformations from Web.production.config to change your Web.config.
We have some documentation about XML config transformations: http://documentation.red-gate.com/displ ... tion+files
There is also an option to run powershell scripts during deployments: http://documentation.red-gate.com/displ ... ll+scripts
Let me know if you have further issues.