Fusible Applique: I like Wonderunder for my fusible and some people like Misty fuse for a softer appliqué. You can use Heat and Bond lite to sew through but don't get regular Heat and Bond. Regular Heat and Bond is meant to stick without sewing and the sewing machine doesn't like it. Most sewing fusibles come with a paper side (where you draw your reverse shape on) and a rough side that goes to the wrong side of fabric. You use an iron to fuse it and when it cools, you remove the paper and it is ready to fuse to the background fabric. I like to use a buttonhole to secure the edge.
The only fusible that fuses on one side only, would be the product that gets fused to fabric for purses? I can't think of any others, maybe someone else can help you with that one.