It depends on what type of applique I'm doing and if I want the stitching to show or not.
If I'm doing a decorative stitch like blanket stitch, I'll use a heavier cotton thread so it shows up more. For a satin stitch, I want the threads to lie nicely next to one another, so then I might use a shiny polyester like Isacord.
If I'm doing the invisible applique using a blind hem stitch, I may use a finer polyester like Sew Fine or Bottom Line, or if I don't want to change thread colors then a clear polyester thread like Monopoly.
Not a very definitive answer, was it??? LOL