You can spin up a cheap VPS in a matter of minutes for less than five dollars. You do not need anything but a credit card usually. If you want a dedicated server all to yourself then it gets significantly more expensive but no less straightforward. If you want to put your own hardware online you’ll have to look at a collocation seller or arrange something with an ISP.

Of course if your home internet connection upstream is good enough, and your ISP permissive enough you could also just do dynamic DNS and have everything running off that.