Let's start by the definitions. Because you're talking about three different fields in the business.
1. VPS: this means Virtual Private Server. And it just means a server that is really a virtual machine. So there is no physical server in the rack but the service provider sells you a virtual machine as a service. See:
https://en.wikipedia.org/wiki/Virtual_private_server.
2. A TOR Hidden Service is a website which is hosted within the TOR network. Mostly these are websites that are run at home. What you do is install the TOR browser bundle, install a local web server, place your website in it and pass the information to the config file of TOR. The TOR software creates a unique id for it. The all known .onion address. Mostly TOR hidden services are used to host content without revealing the location of the website. And it also means that it is necessary to configure the server to give away as little information as possible because this information could be a fingerprint to your location. As you can read, this is a very different world. I don't know if this is applicable for your situation? This is really all I know about this item.
3. Owning domains is relatively simple and is only needed when you host a public website. It's not needed for TOR since TOR uses it's own system to publish your site, .onion adresses. Registering a domain can be done at every provider. Providers often sell packages with hosting and one or more domain names included.
One note on hosting, there is shared hosting and dedicated hosting. Dedicated means owning your own server. This can be a physical one or a virtual machine. That is item 1 in the list, making the circle complete.

TFK