mass - Why are particles different sizes?

Is it correct in saying that a particles size is it's rest energy, and that particles don't actually have size (in the way you get different size objects)?

What defines what sizes a particle can be? Why do particles have discrete sizes, and there's not a continuous spectrum of particles varying in size?

I ask because I was told that particles mass depends on its size, as the bigger a particle is the more it interacts with the Higgs boson and so the more mass it has. So why are there so few particles with specific masses/sizes?