The fabric looks much like some in a string quilt I have made by my grandmother and great grandmother. You probably won't be able to "match" the white as I'm betting it's feed or sugar sacks or possibly other flour sacks.. you could pick which ones you wanted back then. I'm with the others, guestimating the 40's and possibly 30's. I'd use bleached muslin to finish it. sounds like it's similar to (if not totally) English paper pieced. I have made a table topper that size.. my hexagons were the size of nickles by hand. Once you get going and become proficient you'd be surprised how quickly you can zip along. Mine had pale green "garden paths" rather than white. And yes.. I do have fabrics that are 20 years old and more.