There are at least 5 providers that will rent you a $5/month server: DigitalOcean, Lightsail, Linode, UpCloud and Vultr. There's a guy that publishes benchmarks of their $5 instance regularly
https://joshtronic.com/2019/09/02/vps-showdown-digitalocean-...
DigitalOcean is by far the most popular. Personally, I like Vultr because they also have $2.50 IPv6 only instances and you can upload your own ISO file if you want to try a less popular Linux distribution. Both services have similar user interfaces that are pretty good.
That being said, $60/year is still a lot. If you can get away with just a static site, try GitHub pages https://pages.github.com/. You only get one (unless you create GitHub organizations) but it's free. You can still have your own domain pointing to it with TLS (free through Let's Encrypt). You miss out on the fun of managing a Linux server unfortunately.