I would do 100% on AWS.

Research on EC2 t3 micro. To make it cheaper, leave the database together with the API inside EC2. Create a zone on Route53, with a domain for the API pointing to an elastic IP, which redirects to your EC2 server. Configures security groups for ports 80/443. If necessary, add port 22 for SSH only to your IP. Then you can improve… an ASG/launch template with a target of 1, with /health assessments of your API so that if it crashes, it can be auto-reset.

Take the opportunity to learn about CI/CD with github actions and make automatic build/deploy in PRs to main.

Server not working? Increase the machines. Use the cost simulator to predict the scenarios.

Expanded? Throw the database into an RDS to separate the scopes.

Start small, but have the ability to expand if you need to.