For hand applique, I follow the suggestions of Becky Goldsmith and Linda Jenkins (Piece O' Cake): use cotton thread with cotton fabric; try different brands and you'll find one you like better than the others. They like DMC 50-weight and Mettler 60-weight...both machine embroidery thread for hand applique (go figure). They also suggest Aurifil 50-wt 2-ply cotton thread. Match the color of the thread to the piece of fabric that you are appliquing on, not the background fabric.
If you want to do needle-turn hand-applique, I'd suggest getting their book "The New Applique Sampler" and/or their dvd "Becky Goldsmith and Linda Jenkins Teach You to Applique the Piece O' Cake Way". Both are wonderful.