Our quilt guild just made over 900 quilts this last year and 350 tops for charity. Our material sources have been donations from churches, friends, members buying from all of the local fabric places, and sometimes businesses. Our guild sends to shelters, fire departments, police, hospitals, nursing homes, families of the military and the VA hospitals.
Fabric must be clean, unscented, and preferably cotton; although poly/cotton blends are ok for the non-hospital locations. Battings are mostly cotton, but poly, fleece and flannel have also been used for the non-hospital destinations.
Best way to get material - ASK! You would be surprised about the number of friends of a friend who don't sew any more, are moving, just passed away, etc who want their stash to go to a good home, and knowing it is going to a charity really makes the donors and their families happy.
Good luck on your search and let us know what you wind up doing. There are a lot of really good ideas in this post you can use.