When I was in the 8th grade, my lab partner and I had finished with our experiments for the day. I was one of the smarter kids, and he was also ahead of the curve, so we finished long before everyone else. Bored, we then noted that we had a hot plate and some chalk. What was blackboard chalk, anyway? We saw it every day, and still had no idea where it came from. (Besides "schools.") We decided to do an experiment.
We put the chalk on the hot plate, and watched it carefully. Was it an organic compound, that would burst into flames, or an inorganic compound that would melt? (In either case, we watched carefully so that we could quickly unplug the hot plate, extinguish any flames, and cool it back to a safe temperature when needed.) Before we got that far, our teacher interrupted by sending us both to the principal's office for unauthorized experiments, where we both got chewed out. That jerk.
Since then, I've learned that blackboard chalk is Calcium Sulphate, and it is usually made by processing a natural rock called Gypsum, crushing it up and pressing it into a stick. It is inorganic and does not catch fire. It melts at 1460C, a temperature we would not have achieved with a high school hot plate. Gypsum is also processed into Drywall, a housing compound that makes the house more difficult to set fire to, a definitely desired property.
I think it would be nice if there was a lab that just played with materials to invent new ones. The funders would get the patent on anything the lab discovered. Various chemical, nanotechnology, and heating and cooling experiments would surely invent some new interesting material.
Expert researchers would be preferred, because they would already have some knowledge about what kinds of experiments would be most effective, and that's worth the extra cost of hiring them.