I do switch out some of the colors, but there are times when I will use a different color thread than the applique piece. I learned from longarming that thread changes color (just like fabric), depending on what you put it with. i.e. sometimes red and brown interchange well..... I lay the thread across the applique piece and see if it is the look I am going for.
Regarding stitch: sometimes I zig-zag (my least favorite). Sometimes I blanket stitch. Sometimes I use the blind hem stitch. Sometimes...I even do it by HAND! LOL Love doing hand work!