I don't have a whole lot of experience with applique because I am a beginner. But I am on the verge of throwing out all the cotton thread I have. It tangles easily, even with bees wax, and has really made a mess. I haven't used silk a lot because its so pricy, but have used the poly thread and love it. It also disappears into the applique, at least enough for me until I am about to buy and try silk.
Hope this helps as cotton isn't for beginners I don't think anyway.
Rita