The correct service for this scenario is designed for high-speed online data transfer and supports both internet and dedicated network connections like Direct Connect for data migration. It automates the synchronization of data between on-premises storage and cloud storage, making it particularly useful for moving large datasets into cloud services. The Transfer Family service, while it provides secure file transfers into and out of cloud storage, is not particularly optimized for on-premises data migration. The Glue service is primarily an ETL service for data transformation, not data transfer. Finally, the service for streaming focuses on processing and analyzing streaming data in real time and is not the standard choice for batch data migration tasks.