These days, you have many more options with how to set up your ColdFusion environment for efficient use of resources, reliable up-time and security. That isn't to say that all of these will come cheap, but what's nice is that you can be in control of the costs as much as you want...down to the second. While you can still buy your servers and install your own CF apps, it is nice to have choices. The best option these days for the right balance of price and reliability is the cloud. Microsoft Azure, Amazon Web Services (AWS), Google Platform, Digital Ocean, etc are all options that let you do things like set up a VPS or host Docker containers that have your applications built in.
With ColdFusion, you can install it just like it's on your own physical machine. You can use the Adobe ColdFusion installation package or the Lucee installation option. Depending on the OS, you can set up CF behind a web server and you're ready to start. That may mean handling all the configurations, but other than hardware, you have the same level of control as you would get with your own box.