The process is not as complicated as it seems
You need one developer certificate for testing and one distribution certificate for deployment (ad hoc or AppStore). If you have a valid certificate (given that you submitted an app already), then make sure you have it in your keychain (with the private key).
For a new app, you need to create a new appID. Remember that it should match the bundle identifier in your Xcode project.
With the distribution certificate and the appID, you can create a new distribution provisioning profile that needs to be downloaded to your machine. And should be used for the code signing in Xcode.
So, short answer. Use you current (valid) distribution certificate, add a new appID (matching your bundle identifier) to create a new Distribution Provisioning Profile. Use the profile to code signe your project.
Good luck... enrique