Web API Host Options

What are some options for deploying a restful web API built with .Net Core so that other applications can call it at any time? Is there a not-too-difficult way for individuals to setup a dedicated server that can host APIs?

Ideally I'd like to find a hosting service that fits these criteria, but understand that there's probably nothing perfect:

  1. Cheap
  2. Can host SQL databases that the API can interface with
  3. Supports custom domain name configuration

I've had some success deploying to Azure, but this is extremely expensive for an individual dev.