I wouldn't recommend remote desktop. There is not much difference between connecting on a local network or a wan. (Outside network). There are a couple of different setups. Each computer could have a public ip address or just the router/switch could have the public address and then use port forwarding to the local computer - server. You would use the public ip address to access the databases. You would want to security setup on filemaker to keep unwanted users out.
links that may help you setup your network.
I would investigate a FMP Hosting service. $25 to $50 per month for one database.
Response is almost certain to be better, unless you have a fiber or high speed broadband connection.