Elastic Compute Cloud (Amazon EC2) is a web service that provides secure, resizable compute capacity in the cloud. It is designed to make web-scale cloud computing easier for developers.
There are several options when it comes to running Docker containers in AWS:
Elastic Container Registry (ECR) - Easily store, manage, and deploy container images
Elastic Container Service (ECS) - Run containerized applications in production
Elastic Kubernetes Service (EKS) - Highly available, scalable, and secure Kubernetes service
Fargate - Run containers without managing servers or clusters
Note: It is also possible to run Docker (via Compose, Swarm or Kubernetes) on bare EC2 instances.
Virtual servers, storage, databases, and networking for a low, predictable price.
This is likely to be simpler than setting everything up yourself; VPC, Route 53, Elastic IP, EC2, EBS, RDS, etc.
Details about Lightsail can be found at the AWS web page.
Run code without thinking about servers. Pay only for the compute time you consume.
Details about Lambda can be found at the AWS web page.