It can be challenging to hand applique pieces that are fused. There are so many different ways to machine applique fused pieces, if you experiment a little you are bound to find a method that you like.
I found the book by Harriet Hargrave to be very valuable for showing how to do the various techniques. I was able to teach myself using that book. Here is a link to it on Amazon:
http://www.amazon.com/Mastering-Mach...dp/157120136X/
Actually, mine is the older edition of this book:
http://www.amazon.com/Mastering-Mach...dp/0914881450/
I tried satin stitching, but I don't like the way it stiffens the applique.
You do need to use a stabilizer underneath machine applique unless you do what I do -- which is to heavily starch the background fabric first. I use a 1:1 solution of Sta-Flo liquid laundry starch and water, "paint" this on using a large wall painting brush until fabric is saturated, wait a minute to allow the starch to be absorbed, toss in dryer, then iron with steam. This stiffens the fabric sufficiently to eliminate the need for a stabilizer.
You also need to learn about fusibles. I have migrated to using Misty Fuse for fused machine applique work because it leaves the fabric very soft. Heat and Bond, in contrast, stiffens the applique quite a bit.
I have done hand applique (with turned under edges) and love the result. However, my hands and arthritis are such that I cannot use a needle like that for more than a few minutes at a time. Hand applique is slow compared to machine applique.