If by "REST API" you mean that you want to follow a REST architecture then the media type to use is determined by the functionality you want to expose through the REST API. Do you want to be able to create new objects? Query a list of objects? Edit an object? If so, then a good RESTful media type to use might be vnd.collection+json because it defines a hypertext linked interface to manipulate a collection of json objects.
Note: A RESTful API could use the media type application/json, but this media type doesn't have a hypertext linked RESTful interface, so it would be an end point in the state change.
It's also completely acceptable to follow a web API architecture, where HTTP RPC calls return application/json objects, and other HTTP RPC calls manipulate those objects, and there is no hypertext link interface for using and navigating the state changes. But this isn't REST.
I like this description of REST (from the creator of REST):
REST APIS must be hypertext driven
In other words, if the engine of application state (and hence the API)
is not being driven by hypertext, then it cannot be RESTful and cannot
be a REST API. Period.
Also, from the discussion of that post is this example of a RESTful application: Lost Boys's Spam-E REST Application