Exactly what colors you use for painting skin tones and how many is a matter of personal preference and style.
My preferred colors for mixing the full range of skin tones are:
If you don't like using cadmium pigments, substitute whichever red and yellow is your favorite. The advantages of cadmium red and yellow are that they're both warm colors and have very strong tinting strength (so a little goes a long way). It's well worth experimenting with all the red and yellows you have, to see the results you get.
The blue can be whichever you prefer too. I like Prussian blue because it's so dark when it's used thickly, yet very transparent when used thinly.
These are certainly not the only options open to you. Everyone develops their personal preference through time. Experiment with golden ochers, deep purples, ultramarine blue, and greens. Pay attention to the underlying color of your model's skin too (not their dominant skin tone). Is it warm or cool red, blueish, cool or warm yellow, golden ochre, or what? If you have trouble seeing this, have a look at the color of various people's palms and compare theirs to yours.
Color mixing tip: a little of a darker color mixed into a lighter has a much greater impact than the same quantity of light mixed into a dark. For example, umber added to yellow rather than yellow to umber.