If it has an extra 1/4" seam allowance on every piece, some of the smaller pieces may be out of proportion with the larger pieces. For example, a 1/2" hat band with another 1/4" seam allowance is 200% it's regular width, whereas the much larger bonnet with the same seam allowance is maybe only 15% larger.
I would definitely want to lay out all the pieces first to make sure they're going to give you the finished look you want without trimming any of them down, if you're going with fusible. And then I'd go with either Misty Fuse or Pellon 805 and would window the fusible (cut away all but the outer 1/4" before applying to fabric) to make it softer. Typically applique is attached either with a 1/8" buttonhole stitch or a satin stitch, but I've seen ones with zig-zag stitching before & that's cute, too.
The other option you have is to do a turned edge via the freezer paper method. I've done that, tacked the turned edge pieces down with washable glue & stitched by machine. If you can't just use them as is, maybe give this a try!