things that come to mind...
What database app and web server allows users to search, view, etc, the data? That would not be a NAS function. Some server is needed. It is viable to do all this on the NAS itself, but the NAS would lack the sophistication you'd need in order to avoid lots of system development work.
Is the public accessing the data on your NAS, using your ISP bandwidth? Yikes. And it might be a violation of a residential ISP service contract. If not stored on your NAS, then the data is somewhere in the cloud on a server?
Not knowing the essence of the objective.. my first guess is that you should be looking at a hosting service provider, if that cost makes sense. Amazon Web Services is inexpensive. Also inexpensive for backup. But upload speeds from a residence can be too slow.