That's a tough one. My knee-jerk response is to set up a baseportal site like the M0001 Registry database: http://www.mac128.com/m0001
You can force people to register in order to contribute which will cut down on some vandalism, but, as anyone who's ever contributed to a WIKI knows, registering is no guarantee someone won't muck it up. That's why the M0001 Reg. is not editable, only post-able.
This is true even if you were to host a FileMaker database on your own server. Someone would have to police the members allowed to update it.
If I were you, I'd go with the BasePortal model and make it a post-only system that only a few "editors" you decide would have access to to make fixes and changes.
The good news is that you can upload your existing databse as a .CSV file to BasePortal as is.