How to set-up my EC2 server and find the right model for me?

Here are some good resources that you can refer to architect your solution.

1. Use Amazon EC2 for cost-efficient cloud gaming with pay-as-you-go pricing
2. How do I choose the appropriate EC2 instance type for my workload?
3. Choosing the Right EC2 Instance Type for Your Application
4. AWS re:Invent 2020: Selecting the right Amazon EC2 instance for your workloads

As one of the above references says that because you can launch and terminate instances as desired, profiling and load testing across a variety of instance types is simple and cost effective. You can easily change instance types as your needs change. You can even profile multiple instance types as part of your Continuous Integration process and use a different set of instance types for each minor release.

Auto Scaling Groups (ASG) can help with provisioning EC2 easily and it can help you manage the scaling easily so that you don't have pay for EC2 when you don't need them. Also, ASG makes it easy to pick and choose the instances by offering a new feature called Attribute based instance selection. If you want to further cost optimize and if your use-case can tolerate interruptions, then you can leverage EC2 Spot instances. You could also use ASG to mix and match On-Demand and Spot instances as well. There is a lab which explains how to deploy ASG with different options (last link in the reference) which you may find useful.

References:

https://docs.aws.amazon.com/autoscaling/ec2/userguide/auto-scaling-groups.html

https://aws.amazon.com/blogs/aws/new-attribute-based-instance-type-selection-for-ec2-auto-scaling-and-ec2-fleet/

https://aws.amazon.com/ec2/spot/

https://ec2spotworkshops.com/ec2-auto-scaling-with-multiple-instance-types-and-purchase-options.html

There is actually an entire learning plan on skillbuilder dedicated to this:

https://explore.skillbuilder.aws/learn/public/learning_plan/view/1569/aws-for-games-learning-plan-game-servers