Have it hosted on a Filemaker Database Hosting Service ($30 to $50 per month) allowing FMP or web browser access or both.
Share it from your server, set your router to portforward.com any FMP requests to the server's local IP address. This means each remote user will need a copy of Filemaker.
Share it from your server with Instant Web Publishing or Custom Web Publishing, remote users would access the database with a web browser. The database would have to be designed with the limitations of web publishing in mind.