White, black and greys

Hi.
How should I include some grey and black color in to a color palet (which also inlcude blue)? I mean, if I include some gradient of grey, the white and the black, I should not worry too much about about the other two colors, right? If I choose a red and green only, just those two are going to vary according to any RULE, and doesn't affect to the greys, blacks and white?

So, should I include greys, black and white on the pallet? Or the palet is just for RGB with medium/high saturation? Orientaitons, please.