Which one saves more money:EC2 shutdown, snapshot, or AMI?

Keeping an AMI would probably be cheaper because it's using S3 on the backend vs EBS on your EC2. If you are fine with it taking slightly longer to spin up when you go to use it again I would go with AMI.

The most cost-effective approach for your situation depends on various factors such as how frequently you use the EC2 instance, the duration of non-usage, and your specific storage requirements.

If you rarely use the EC2 instance and want a quick and simple way to stop incurring compute costs, option 1 (EC2 shuts down) is straightforward. If your goal is to reduce EBS storage costs and have a backup of your data, options 2 (Snapshot and Delete EC2) or 3 (Ordinary AMI and Delete EC2) are suitable. Snapshots and AMIs allow you to recreate the instance if needed. If you want to store the AMI in a low-cost storage solution, such as Amazon S3, and still have the ability to recreate the instance easily, option 4 (Store AMI to S3 and Delete EC2) may be a cost-effective choice.

Before making a decision, you should calculate the costs associated with each option based on your usage patterns, storage requirements, and the specific pricing details for each AWS service. AWS Pricing Calculator can help you estimate costs for different scenarios. Additionally, consider factors such as data retention policies and the ease of instance recreation when choosing the most suitable option for your use case.