There are so many ways to applique...first you will want to decide if you want to applique by machine or by hand. You can find methods for both that have visible stitches or not. Machine applique had many variables, and a lot may be determined by the sewing machine that you have. When I bought my machine 20 years ago, I knew I wanted a machine that does the blanket stitch, and I do most of my applique with that. It is a fusible applique, but I use the fusible just around the outer 1/4" edge, the center stays soft that way, not stiff from the fusible. I also like doing the "mock-hand applique" which I do using freezer paper, and a very narrow blind hem stitch with invisible thread. Satin stitch if done well looks great, but it takes more time, more thread, and you really need to use a stabilizer for it to look good.
Maybe make some samples of different kinds of applique and see which you prefer.