The correct approach involves creating a shutdown script and assigning it as a metadata entry with the key ‘shutdown-script’ in the Cloud Platform Console when setting up the virtual machine instance. This method ensures the application can shut down gracefully upon pre-emption. Other methods, such as using the CLI, Console, or API for shutdown commands or workload migration, introduce unnecessary complexity and do not guarantee a graceful shutdown. The deployment manager cannot be used to set a shutdown script as a metadata entry, making the Cloud Platform Console the appropriate tool for this purpose. Reference: Google Cloud Documentation on Shutdown Scripts.