Hi Carla,
At one time they used an all cotton lining, now it is up to your discretion, nothing wrong with the blends.
Usually if fabric has a very white color or background they use white, if color or off white they use ivory, natural, off white.
JoAnn's and many other places usually have the linings on sale often.
Make sure that your silk and whatever your lining choice it is steamed or pressed well before sewing, they allows for some shinkage.
Have never tried the sheets, may work others might have more input.

After going through all the work you do not want one fabric to shrink when drycleaned and the other does not.

Hope this helps a little. Patti

If you don't want to use the drapery lining sure you can use sheeting. Before you buy sheets however check fabric stores for sheeting fabric. and make sure it has some polyester in it so it doesn't shrink. Sheeting comes in widths of 98 to 108 inches so you can use the width as the length.