Mops has given you your answer - now a question for you! Have you posted a picture of your Secret Santa gift?
I don't think you HAVE to use a specific one, all sorts of embroidery threads can be used, it's just a matter of taste. If you want it shiny use polyester and viscose/rayon. Cotton (and there's a dull variety of polyester on the market too) will give a heirloom effect.
I used rayon for my butterflies and gold metallic for cards.