I love to applique.....and have done much of it over the years. Two things that I think are so important.....use something that doesn't fray so you don't have to worry about turning under the edges. The other thing is ...you don't want to it to look worn after a few years.
WOOL MELTON IS THE ANSWER
Felt has often been used but felt is not a woven fabric, it is pressed fibres so it will not hold up like the woven melton fabric. Remember the appliques on older parkas?? The felt had worn and the applique was raggy looking.
Here is a selection of items I have appliqued over the years. The process is simple. Iron on a fusible adhesive (I use Heat and Bond Lite) to one side of the melton (there really is no right or wrong side). Trace or draw your desired shape onto the paper side, cut it out, and place it adhesive side down to your base and press. To secure it either straight stitch around the edges or do a narrow zig zag.I don't use a satin stitch as it takes too long but if you want to do it, it looks great. I also recommend using invisible thread for your top thread so you don't have to keep changing thread.
Below is a couple of cushion covers that i just finished from melton scraps, attached to the base of white melton with the heat and bond and stitched down with a straight stitch. I used our #873 FOLK ART pattern for the first and #833 IF THE SHOE FITS for the second one.