We use the numerically exact superposition T-matrix method to compute electromagnetic scattering characteristics of a macroscopic volume of a discrete random medium filled with wavelength-sized spherical particles with a refractive index typical of water ice at centimeter wavelengths. Our analysis demonstrates relative strengths of various optical observables in terms of their potential remote-sensing content. In particular, it illustrates the importance of accounting for the forward-scattering interference effect in the interpretation of occultation measurements of planetary rings. We show that among the most robust indicators of the amount of multiple scattering inside a particulate medium are the crosspolarized scattered intensity, the same-helicity scattered intensity, and the circular polarization ratio. We also demonstrate that many predictions of the low-packing-density theories of radiative transfer and coherent backscattering are applicable, both qualitatively and semi-quantitatively, to densely packed media.