I haven't done enough applique to give advice, but I researched it quite a bit when I did a project (quilt and cushion covers for mt grand nephew).
What I tried and tested was using paper backed fusible web to stabilise amd keep the applique in place.
In the pictures the glasses are appliqued on, I used paper backed fusible web, and stitched them on using satin stitches (a narrow zig zag stitch).