When migrating a database to a PaaS offering, the primary concern should be the compatibility between the on-premise database and the cloud provider's service. If there isn't compatibility, the database may not function correctly after the migration, leading to data loss or application failure. Ensuring compatibility encompasses the database schema, data types, stored procedures, and any specific database features used on-premises that must be supported by the PaaS offering. Checking for performance considerations is also essential, but it is secondary to ensuring compatibility. Understanding the service-level agreements (SLAs) is more about ensuring the cloud provider will meet the company's requirements after the migration, not about the migration process itself. Lastly, total cost of ownership (TCO) reduction is a goal of cloud migration but does not primarily ensure the success of the migration process.