And when it dries you can paint it whatever colours you want
Some air-dry clay IS white although the most popular brand is terracotta - dull red. You can paint it to your heart's content.
Yes, you can paint air-dry clays any color you want, and many of the craft air-dry clays are already white. If the clay itself isn't white, it may be first coated with white paint so that any colored paints used on top later that will show up as their true colors (and brightest version). Special white paints for doing that may be called primers or gesso (in white). Some brands of paint are higher-quality and have more pigment than others, so the cheaper ones may require two coats for best coverage (and some of the cheap reds may bleed even if they're permanent ones). Air-dry clays can be painted with any kind of paint, but the most common might be permanent paints like acrylic paint or latex paint, or even spray paints of all kinds. Non-permanent paints like watercolor paints and tempera/poster paints would need to be sealed (usually with a clear permanent sealer) to keep the colors from running with later exposure to moisture. Common permanent clear sealers are Mod Podge or just any thinned PVA white/craft glue like Elmers Glue All, acrylic mediums, etc, but the toughest will be polyurethanes (from the hardware store).
