I think this helps me clarify what I am asking: I want to set up an instance of Matrix/Element that is private (defederated?).
To do so, it has to live somewhere. And I gather that can be a public server like @domi linked to, or on a VPS (or physical server, but I don't want to go there).
Public server is what I originally had in mind: are there any that are better options than others in relation to security/privacy?
If I instead rent space on a VPS, (a) what's a decent one to consider and (b) do I then need to install something in addition to Element like Synapse, which someone else mentioned?