There's several ways of painting white. You can lay down a coat of blue-grey, or more of a pure grey, you can also use something like a cream colour or a greyish brown which I think looks more natural.
You can also just lay down a coat of white and then shade it and highlight it again to bring back the whiteness.
Regardless of which method you pick, you are going to be doing lots and lots of thin coats in order to get a nice solid cover over a black primer.
If any of my models has any significant amount of white I will consider priming white (or light grey) instead of black, even if the model is mostly dark colours, it's far easier to make a white undercoated model dark than it is to make a black undercoated model have a vibrant white.
I actually very rarely prime black any more. The only models I've primed black in the past few years have been my
40k Aeronautica Ork vehicles because they are 90% black and my Night Goblins because, of course, they are mostly black