Ordinary paint can go a long way. But we also use home-made recipes like salt paint, puffy paint, or "goop." If you would like to try these at home, you might check library resources such as The Ultimate Book of Kids Concoctions, by John Thomas and Danita Page, or Pam Schiller's resource book series.
What about the mess? We provide smocks to (mostly) protect children's clothing, cover the floor when an outdoor space is not available, and generally expect that there will be some clean-up involved during and after the session. Meanwhile, the children and their grown-ups get to use their senses, build some vocabulary as they talk about what they are doing, practice their motor skills, and have a good time. We think it's worth it!