Hi Addlee,
Thanks for your messsage. Your squares should make a beautiful quilt. Just be sure you soak and rinse lightly your squares before quilting and making your "sandwich" (quilt top, batting and backing). Muslim will shrink, unless your mom washed the muslim before she used it to embroidery on.
Amazon.com has several books out on quilting in sections and I think I mentioned them in a message to Becky on Page 3, of this particular subject. There are lots of ladies that have written books on this way of quilting and I, too, am going to try it. Local quilt shop is even going to have a class on it so will try that first. Don't know where you live but if you have a quilt shop you go to you might ask if they have a class in this. I think other folks in this column have mentioned Betty Cotton, who sounds like she is very good, too. You can get her books on Amazon.com, too.
As for batting, a friend recommended using Warm and Natural, 100% cotton for 4 lap quilts I am making that I want to be light and yet comfortably warm. It seems to be just perfect on the ones I have finished so far. Just remember, if you want an antique look (crinkly) to your finished quilt, don't soak and dry your batting beforehand. If you want your finished quilt to look smooth after you finish, then pre-soak and lightly spin dry and dry on low heat. Smooth out and fold before using the batting .
Hobb's makes a wonderful batting that is 80% cotton and 20% polyester that is really nice, too, for regular sized quilts or ones that you want a little thicker. Washing before or after quilting is the same results with Hobb's. My personal favorite for all around is the Hobb's 80-20. Think I will stick with it from now on.
If you're looking for a marvelous, all-around excellent quilting booking that covers everything from A-Z about quilting, Better Homes and Gardens has a wonderful big, thick book that is easy to read and understand. Better than Quilting for Dummies!! I got mine at BooksaMillion but you can get a lot cheaper at Amazon.com under the new and used books.
Hope I was able to help you out a little. I'm no expert but have had some wonderful teachers, so glad to pass on any of the "good stuff" I have learned.
Good luck, Addlee! Norma