For all skin colors I use the same basic palette
Quinacridone rose
new gamboge
cobalt
burnt sienna
indigo
white and/or off-white in acrylic
Caucasian skin can made with just quin. rose and new gamboge in various mixtures. I also sometimes add a touch of cobalt or burnt sienna if needed (since there are tons of different skin colors in each 'type' of skin). I sometimes use white and/or off-white if I am painting with acrylic thicker than is typical for me.
African American skin can be made with quin. rose, new gamboge, burnt sienna, and a little cobalt. I also add indigo for shadows or in the skin color if it is very dark skin (again, since there are tons of different skin colors in each 'type' of skin).
All of the other types of skin are made with the same 5 - 7 colors in different combination.
I use these same colors for both acrylic and watercolor portrait and figure paintings. I also work in colored pencil with Prismacolor pencils and use peach, light peach, white cream, thio violet, canary yellow, true blue, burnt sienna, dark brown, indigo in various combination for the skin colors.
I prefer Daniel Smith for watercolor paint, Golden Acrylic for acrylic paint, and Prismacolor for colored pencils.