For the more technically inclined gamer's, DigitalOcean can look like a good choice for hosting a Minecraft server. It is cheap, offers hourly billing and their VPS's can come pre-installed with Minecraft Java.
When deciding your Factorio Server Hosting provider, you are going to see a lot of different providers. Factorio is a hugely popular game, and it shows. Close to 20% of all servers on the ServerFlex network are Factorio servers!