The correct choices are Configure an AWS Site-to-Site VPN between the data center and the VPC and Run the workload on Amazon ECS with the Fargate launch type in a dedicated VPC. The Fargate option minimizes infrastructure management while the Site to Site VPN option provides encrypted connectivity so the application can reach internal systems securely.

Run the workload on Amazon ECS with the Fargate launch type in a dedicated VPC removes the need to provision or manage EC2 hosts for the container runtime. With Fargate you define tasks and services and AWS handles the underlying compute, scaling and patching which matches the team goal of minimal operational overhead.

Configure an AWS Site-to-Site VPN between the data center and the VPC provides IPsec encryption for traffic between the on premises network and the VPC and integrates with VPC routing and security controls. This gives a managed, encrypted path so the migrated service can access internal systems without exposing traffic to the public internet in plaintext.

Migrate the containers to Amazon ECS on the EC2 launch type in a dedicated VPC is not a good fit because you must manage EC2 instances for capacity, patching and scaling which increases operational burden and contradicts the minimal management requirement.

Front the service with a Network Load Balancer using IP targets and an HTTPS listener is incorrect because a load balancer does not create an encrypted site to site link to on premises systems and Network Load Balancer operates at layer four rather than providing application layer HTTPS handling like an Application Load Balancer. A load balancer also does not replace the need for a secure connection between the data center and the VPC.

Provision AWS Direct Connect for the on-premises link and use it without additional encryption does not meet the encryption requirement because Direct Connect connections are not encrypted by default and you would still need to overlay IPsec or another encryption mechanism to protect traffic that must be encrypted end to end.

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