If you're deploying applications on AWS one of the easier ways to get started is to simply deploy everything on EC2. If you're not familiar with AWS EC2, EC2 instances are compute instances. They are like your (linux) desktop, except that yous spin them up and kill them on demand with AWS console (or CLI or some other infrastructure automation tool).

Should I use EC2 to Deploy my RShiny App?

If you're looking for a solution that has some built in scale and ability to throw a Load Balancer at it EC2 is fine. It's also nice because it's just a computer. You don't have to find a work around to get you a computer the way you do with Docker (docker run) or Kubernetes (kube exec). You deal with an EC2 instance the way you would any remote server, but its on AWS so you get some additional niceness such as the backups, Elastic IPs, and Load Balancers.

This is slightly more difficult than using LightSail. If you are completely new to AWS and on a tight deadline you may want to start there....