are you doing raw edge applique? you could use fusable--like heat & bond lite- then a button hole stitch or small zig zag works well-
if you plan a satin stitch a stablizer is necessary to keep the blocks from puckering- it is your choice whether or not you want one to stay in (adding a layer & weight) to your quilt blocks- or a removable (there is tear away or wash away) do they have recommendations included with the pattern or book? generally the designer/author suggests what works best...i would follow those recommendations