I've black-primed my mini. I like it because it serves as a free level of shade and is more forgiving if you miss a part of the mini with your paint. White primed yields bolder and brighter colors, but you absolutely have to cover the entire model with paint.
I follow the Foundry System (though I use Reaper paints.) The Foundry system is based on the three-palette color: A color, it's base shade and its highlight. You start with the shade, then paint the main color over this, then add the highlight.
Throughout this tutorial, I refer to the next shade lighter (of a base color) as a step. So if I say paint something two steps higher than the base color, I mean choose a color that's two shades lighter. Of course, this is relative and based on the paints you use.
So let's get started! (NOTE: You can click on the pictures to get larger versions if you need to see better details.)