Thank you for your post.
FileMaker Pro 14 is capable of hosting to 5 other devices at a time. FileMaker Server 14 can potentially host to as many devices as you'd need. Both options would only require one machine (though two-machine deployment is an option for FileMaker Server), which would also only require one copy of your solution.
For more information on Sharing and related information see Knowledge Base Article #6095 and the "General resources" listed there.
I hope this helps!
When hosting with FMP, any of the computers could be the host. It is recommend to used the same machine to host the database each time. The clients connect to the hosted database by using "open remote" with in FM. FM own networking, Do not use any other networking to open the database or open the database without using open remote from a client machine because it could corrupt / damage the database. The machine that opens the database first is consider the host computer, but again it is recommend to use the same machine to host the database.
If hosting with FMS then each computer would connect with "open remote".