Is there a preferred/recommended Internet Media Type for RESTful POST requests?
No there isn't. Use the media type that is most convenient for the clients that need to access the API.
With that said, you should always strive to use well-standardized formats, like XML or JSON or application/x-www-form-urlencoded to reduce the amount of work needed in the client. Additionally, if the API is meant for use outside your organization, you'd want to accept requests in multiple media types to let the clients choose the one that's most convenient for them; require the client to send Content-Type header in their requests so the server know how to decode the request body.
or does REST recommend I send the data as whatever format the response is going to be sent as (e.g. JSON/XML)?
There isn't any requirement for request body to have the same content type as the response, nor any need to. A REST client should send a Content-Type header to specify the request's media type and Accept header to negotiate the response media type.