My favorite method for turned-under machine applique is freezer paper applique, which is explained in detail with photos in any of Harriet Hargrave's editions of "Mastering Invisible Machine Applique". Here is a link to the latest edition on Amazon:
http://www.amazon.com/Mastering-Mach...dp/157120136X/
This book (or any of its older editions) is well worth the money if you want to learn which applique techniques work for you! This method works well for both large and small pieces of applique.
If you want to use a fusible for applique, my recommendation is Misty Fuse because it does not add stiffness. The same parchment paper I use for cookie baking works great for keeping this fusible off my ironing board and iron. This method works well for small details, with satin stitching to secure the edges.
One thing I do is eliminate the need for stabilizer by heavily starching the background fabric for machine applique. My method for yardage is to mix a 1:1 solution of Sta-Flo liquid laundry starch and water, "paint" this on the yardage using a large wall-painting brush, toss in dryer, then iron with steam. All of this before cutting out the background pieces. (It's a good idea to always cut background pieces an inch larger than necessary, then cut to size after you applique. However, I have not found this necessary when I use the starch background fabric.