Hiya, John -
I'm working with a nonprofit now on their installation of M-Files, which is a highly-capable document management system with a hosted version. Their key value lies in how easily M-Files manages metadata, a critical feature for document management.
Lighter/leaner solutions we looked at during the evaluation phase included:
Shelf (shelf.io) - Affordable, easy to use, nonprofit pricing available
Box.org - Closer to a file share solution, but they're adding more document management features all the time.
SharePoint online - Also affordable, recently much improved, and tightly integrated with Word, Excel, etc.
These are just a few, top-of-mind solutions out of the 85 we reviewed. It'd help to know more about your objectives, of course, before making a recommendation, but I hope this helps as a starting point and feel free to reach out if you'd care to discuss in detail!