If you measured all the related to motion and all the stored energy in the particles of a substance you would be measuring?

Answer 1

I would say non-relativistic total energy. The energy related to motion is kinetic energy; The stored energy in the particles is potential energy.

Answer 2

The stored thermal energy in a certain body (or the stored heat if you like) is the product of its specific thermal capacity and the temperature difference between its temperature and ambient temperature (assuming the observer is at ambient). The specific thermal capacity is the specific heat per unit mass of its material times the mass, if there are different components of different materials you just add them arithmetically.

The above works when there is no change of state, ie always a solid or a liquid or a gas. If there is a change of state, like water turning into steam, then there is also latent heat to include.

Heat is due to particle motion as your question indicates, but we don't measure that directly.

Answer 3

You would be measuring the kinetic energy (related to motion) and potential energy (stored energy) of the particles in the substance. Kinetic energy is the energy of moving objects, while potential energy is the energy stored in an object that can be released in the future. By measuring both, you can understand the energy state of the particles.