I was going to recommend the same book.
If you feel there is monetary value over, say, $400 to your family quilt, you might want to have an appraiser evaluate it first. Sometimes repairs DE-value these older quilts. Many, many of them are less valuable than we think or wish they would be, so repair in order to save them for passing down in the family is a very good, respectful idea.
By the way, the "netting" you are referring to is called crepeline and is a silk organdy material that is nearly invisible; used by museum restorationists, it may not be absolutely necessary in your project as it's quite expensive. You could use the finest weight, smallest hole bridal tulle you can find instead.
Jan in VA