I is your choice. Most quilts now are like you said ,cut 2 1/2. I some times cut 2 1/4 inches, depending on project. I have done some wider if I want it more like a border, but ususally use narrow esp. if matching outer border. I do have an old quilt from GGM, but she folded back to front since it matched sashing on quilt. I think the important part of binding is that it is even on both sides and filled with batting to edge.
GGM's quilt binding was about 1 1/2 inches wide