I agree with all the comments on this lovely quilt and hand quilting will make it even more beautiful. I too would not wash it before quilting for the same reasons given, it could get damaged in the washing machine. If you could find a fabric of that period to put a border on then I think that would be alright but would take away from the antique quality. I too would put a unbleached muslin to back it and to bind it with. I have hand quilted many older quilts for other people and sometimes they are very fragile.
And how lucky you are to inherit this lovely piece of family history.
Pat
homecaregiver