Need some help for choosing the replication type
In the simple view, this pretty much looks like Transactional Replication from {Publisher1, Publisher2, Publisher3} to Subscriber.

I assume that Subscriber includes the Staging DB.  Therefore, as the Staging DB is updated it can, in turn, become a publisher using Transactional Replication to {Subscriber1, ..., Subscriber5}.

Of course, depending on the way data is maintained, you might need to use Merge Replication instead. 

Paul Ibison has a brief article that discussed the differences in republishing with Transactional or Merge Replication at: http://www.replicationanswers.com/Republishing2005.asp

The big issue is being sure that you clearly understand which sources of data are authoritative, how the data flows (and what happens to it in the Staging DB), et cetera.