Energy may be a property of matter, but it's a property of radiation, too! As the universe expanded, the energy density of radiation has decreased by (linear scale)^4, while the energy density of matter as decreased by (linear scale)^3, so in the early universe, the radiation energy density was much higher than the matter density. So you could say, in a way, radiation preceded matter. But you'd better know the details.
I think matter technically refers to massive things composed of fundamental fermions, like electrons and quarks, and the forces that hold them together. Radiation usually refers to light and also matter moving at relativistic speeds. (At relativistic speeds, most of the energy is in kinetic energy, whereas in ordinary matter, most energy is in rest mass.)