We analyze the packing properties of simulated three-dimensional polydisperse samples of spherical particles assembled by mechanical compaction with zero interparticle friction, leading to random close-packed configurations of the highest packing fraction. The particle size distributions are generated from the incomplete beta distribution with three parameters: A size span and two shape parameters that control the curvature of the distribution function. For each size distribution, the number of particles is determined by accounting for the statistical representativity of all particle size classes in terms of both the numbers and volumes of particles. Remarkably, the packing fraction increases, up to a small variability, with an effective size span, known as the coefficient of uniformity, that combines the three control parameters of the distribution. The local particle environments are characterized by the particle connectivities and anisotropies, which unveil the class of particles with four contact neighbors as the largest class with an increasing population as a function of size span, indicating the higher stability of particles trapped by four larger particles. As a result of increasing topological inhomogeneity of the packings, the force distributions get increasingly broader with increasing effective size span. Finally, we find that larger particles do not always carry stronger average stresses, in particular when the particle size distribution allows for a sufficiently large number of small particles.