It depends a lot on what fusible you are using. Some fusibles stiffen up applique pieces quite a bit. I would classify Wonder Under and regular Heat n Bond as stiff. When using these, especially on large pieces, you want to "window" the fusible, leaving it only around the edges. A soft fusible such as MistyFuse does not stiffen the applique pieces, so there is no need to "window".
MistyFuse is a very lightweight fusible web that does *not* come with a paper backing. However, it's pretty easy to add one. Just iron the MistyFuse between two pieces of parchment paper and then, while the fusible is still warm, peel off one of the pieces. You now have paper-backed fusible! I have not done this recently, so I'm not sure what kind of marker would work on parchment paper. Maybe someone else knows. I would probably cut out the shapes I want in freezer paper and iron those on the right side of the fabric before cutting out. When you are ready to fuse the applique to the background fabric, peel off the paper backing of the fusible.
If you are not sure how stiff a fusible will be, buy several and compare practice pieces. You can tell quickly whether the fused applique is stiff or not, and how stiff.
Edit: Are you intending to sew around the applique edges? The fusibles that don't require this are generally quite stiff. If you use something like MistyFuse, you really need to sew around the applique edges.