For ~4€/month (depending on your country), Hetzner offers "Hetzner Cloud" servers with 2GB of RAM, see https://www.hetzner.com/cloud?country=us
Hetzner has such a VPS offering (2GB RAM/20GB nvme SSD/20TB bandwidth), netcup has one for ~3€, contabo has 8GB/50GB nvme/32TB for 6€/month and there are plenty of smaller companies around the world offering similar deals (usually somewhat less included bandwidth outside europe though).
EDIT: Personally I pay 9-10 EUR per month to Scaleway for a 2G RAM and 2 CPU VPS, private docker repo and S3-compatible storage which holds data and some backups, which run both my personal services and some toy projects when needed. I am not affiliated with them in any way
As for costs, setting up billing and usage alarms on AWS is absolutely trivial.
Finally, using stuff like S3 or dynamo for storage gives me a peace of mind I will never have when managing my own servers.