Fusible webbing is a quilter's best friend when applique is involved. Wonder Under is a fantastic product. I use a small zig zag stitch, satin stitch, buttonhole stitch on my applique and so far, knock wood, it has proven to be the right choice. Also if you use wool felt for your pieces, something not always the best choice, then you have no worries about frayed edges. Take a look at Becky Goldsmith's "Applique The Piece o' Cake Way" as it is an excellent guide.