My favorite applique method is invisible machine applique using freezer paper. Learned how to do it from Harriet Hargrave's book (although an earlier edition than this one):
http://www.amazon.com/Mastering-Mach.../dp/157120136X
I've tried most other methods. Found that my hands are not suited to needleturn applique; fingers cramp up quickly. I don't like the stiffness that fusibles add to applique, although I haven't tried the newer ones like MistyFuse that are supposed to be light as a feather. I get impatient with the time it takes to satin stitch around appliques, plus it takes a lot of thread. I found that the turning method (a la Eleanor Burns and dryer sheets) works only for larger applique shapes, plus I'm not very good at turning the shapes without poking a hole somewhere.
Applique technique really comes down to individual preference, I guess.