You're overthinking this.
There are several components to MVVM:
View:
The view provides a, well, view on the data. The view gets its data from a viewmodel
ViewModel:
The viewmodel is there to organise your data so that you can organise one or more sources of data into a coherent structure that can be viewed. The viewmodel may also perform basic validation. The ViewModel has no understanding of the UI so should not contain references to controls, Visibility, etc. A viewmodel gets its data from services.
Services:
Services provide data from external sources. These can be WCF, web services, MQ, etc (you get the idea). The data the service returns may need to be shaped so that it can be displayed in the UI. To do this you would take the raw data from the service and convert it to one or more Model objects.
Model:
A model object is an object that has been created so that it can be easily displayed/work with the UI.
You may find that you don't need to shape your data coming from your services (lucky you), in which case there's no need to create model objects. You may also decided that you don't want your services talking directly to your viewmodels but instead what to have them get their data via a "mediator" object. That's also good in some situations (usually when you're receiving a continuous stream of data from a source/multiple sources).
MVVM is a bit like porridge: there are lots of potential garnishes you can add, but you don't necessarily need to add them all. Or want to.
Does this help?
Edit: just stumbled on this: a more in-depth expression of what MVVM is:Mvvm Standardisation. This may also be useful