You can use any combination of colors for a color-field painting, though some combinations will work better than others. Analogous colors, for instance, will harmonize together rather than clash. Transparent colors rather than opaque make it easier to get a depth to the color from multiple layers.
It's an opportunity to become intimately familiar with a particular color, indeed with a specific brand of a particular color. While tubes may say they contain the same pigment, there's always a difference, albeit slight.
Look closely at the photo. The canvas has three vertical bands of cadmium orange from three different acrylic paint manufacturers. The bands are painted with the paint at the same consistency in one layer. Yet the middle band is darker in tone. It's not the result of editing the photo, it's the result of three different tubes of paint. Yes, it's a subtle difference, but successful color-field painting relies on noticing such subtleties.
How many colors you need is determined by the number of areas of color you have planned in your composition. There are no right or wrong choices, rather it's a question of your personal preferences, what looks pleasing to you. I suggest starting with two or three areas of colors, using analogous colors, one darker and one lighter.
You also need to decide what color you're going to use for the underpainting. This initial layer of color will influence all subsequent layers (which is where color-mixing knowledge as applied to glazing reveals itself to be a crucial part of color-field painting).
I suggest using a red and yellow, plus blue for the underpainting (like phthalo). If in doubt about what colors to use, do a few studies in a sketchbook first. Don't rule out semi-transparent or thinned opaque colors entirely as options, just be careful you don't unintentionally obscure what you've already painted.
