I'm just teaching myself also and just finished doing the applique on one quilt. Here's what I did and had no problems....(well, except for my ugly stitches)
I always prewash my fabrics (including the applique fabrics)
I spray starch the wrong side of the fabrics blend in with my hands then press, flip over (no need to spray again just press) and have no problems with flaking.
I use double sided Wonder Under, press on the applique fabric, cut, peel off the paper backing and iron on the applique. (The spray starch didn't hurt this process for me at all)
I use the satin stitch on the applique part.
Now if I could just do a better job with the look of my stitches.lol I'm working on it!
I did try the stablizer (copy paper) on a few pieces and really didn't notice a difference. Maybe just try the spray starch and see if it will allow your applique to stick and maybe help stiffen things up enough to sew the applique on. (if you do use the paper as a stablizer with the satin stitch it brakes right off).
Best wishes for success!