use a light wt Misty Fuse for your applique and then your blanket stitch. Or if you want the edges to be turned under, sew that French Fuse (? think that's the name) which is a light wt. knit fusible--you can sew it to the applique right sides together, slit the Fusible and flip and press(use a pressing sheet)
I rarely quilt though an applique unless I'm adding to the design (i.e. pebbling in a flower center, or vein lines in a leaf, etc).