For caucasian skin, I have a very simple recipy that has served me very well over the years:
I tend to undercoat in white, so I'm going with the assumption that we're working form a coat of white primer here, although I've recently also done this without ill effect over a grey primer. Over black, I reckon you'd need to repeat the basecoat step a couple of times to get a smooth and vibrant colour.
Basecoat: I used to work with Vallejo Game Colour Filthy Brown (72.037), but Vallejo changed their colour recipy some years ago, and it's now a lot more yellow than it used to be (used to be a bit more desaturated). I guess the new formula would still work, but I've recently switched to Vallejo Game Colour Bronze Flesh (72.036) and this works every bit as well.
So a basecoat of VGC Bronze Flesh. Then a wash of thinned down VGC Leather Brown (72.040). Several very thin layers preferable over one thicker layer, obviously.
Then a cleanup with VGC Bronze Flesh en then a gradual highlight of progressively lighter mixes of VGC Bronze Flesh and your choice of white paint (I tend to use VGC Dead White, VGC White Primer and Vallejo Model Colour White intermixed; as long as it's white, it's right
).
Finally, I usually use VMC Brown Rose (70.803) to lightly glaze the cheeks and bottom lip of faces and sometimes also the elbows, knees and knuckles (when bare on the model). Same goes for possible scars, although I tend to go a bit heavier there.
And that's it! 3 or 4 colours is all you need for caucasian skin tones. For asian skintones, I do the exact same thing, but change out VGC Bronze Flesh with VGC Plague Brown (72.039)