Sandra,
I cannot think of many applications for stabilizers in quilting, perhaps because I rarely use them.
I use freezer paper (purchased at the super market) on the back of muslin when I make a label. Simply iron it onto the muslin and write or draw slowly. Use freezer paper to draw an applique shape, add the seam allowance, cut out and stitch.
If I have a fabric that is thin, I will use it with a piece of muslin behind - in other words two layers. OR I will spray a fabric without body, with starch or sizing. Spray starch on the back of your fabric as it often leaves a residue.
Hope this helps. Suzanne