I think you need to talk to HostGator. Are they a hosting service that offers to host FileMaker databases specifically?
Do you intend to publish your database to the web so that users can use web browsers to access the data base or will all users have copies of Filemaker installed on their machines (Computers, iPads, iPhones...)?
Your hosting provider needs to specifically support FileMaker databases for you to be able to host with them. I'm pretty sure HostGator does not.
My company does provide FileMaker hosting. If interested, contact me privately.