To allow instances in a private subnet to initiate outbound traffic to the internet without allowing inbound traffic from the internet, a NAT gateway or a NAT instance can be used. The NAT gateway is a managed service that provides better availability and bandwidth compared to a NAT instance, which is self-managed and runs on a specific EC2 instance type. Internet Gateways are used to provide a target in route tables to allow instances to connect to the internet, but since they allow bidirectional internet access, using them alone would not meet the requirement of keeping instances private. Similarly, a Virtual Private Gateway is used to connect a VPC to an on-premises network via a VPN connection and doesn't facilitate private instances accessing the internet.