Programming

I think you want to host a website/an webserver: I would recommend to rent a VM server, nothing expensive, 5$ somewhere. Use Linux, any Linux is fine. If you are a beginner, try using Ubuntu since there are plenty tutorials, guides, questions and answers. You can decide if you want to host your service directly on the Maschine using a builded application (search online for .net core build and host) or using a dedicated docker container on your server. Microsoft provides good resources and boilerplates for both. I personally like the docker way cause it requires less installation and maintenance of the VM server, but if you are unfamiliar, maybe try the direct way. Therefore you will need to install some software, basically you will do what the docker container may already provides, but the application has to be builded and executed anyways. If the application is hosted, you probably want something like an nginx or apache2 server to actually host this application on port 80/443 on your Maschine, then it should be available on the IP of your server. Try searching online for a guide how to sett this up. If you want you can also buy a domain and assign some records directing to your server ip, and you will have an domain name with your service on the internet. Congratulations.

A cheap Linux VPS works for services. For example 3€ per month. With fixed cost cost can't spiral.

If you go for cloud hosting with dynamic pricing you can ensure they have cost limit settings too.

I host stuff on my own VPS. Web services behind an Nginx webserver/reverse-proxy.