Recent modeling of hydrogen-rich Type II supernova (SN II) light curves suggests the presence of dense circumstellar material (CSM) surrounding the exploding progenitor stars. This has important implications for the activity and structure of massive stars near the end of their lives. Since previous work focused on just a few events, here we expand to a larger sample of 20 well-observed SNe II. For each event we are able to constrain the progenitor zero-age main-sequence (ZAMS) mass, explosion energy, and the mass and radial extent of the dense CSM. We then study the distribution of each of these properties across the full sample of SNe. The inferred ZAMS masses are found to be largely consistent with a Salpeter distribution with minimum and maximum masses of 10.4 and 22.9 M ⊙, respectively. We also compare the individual ZAMS masses we measure with specific SNe II that have pre-explosion imaging to check their consistency. Our masses are generally comparable to or higher than the pre-explosion imaging masses, potentially helping ease the red supergiant problem. The explosion energies vary from (0.1-1.3) × 1051 erg, and for ∼70% of the SNe we obtain CSM masses in the range between 0.18 and 0.83 M ⊙. We see a potential correlation between the CSM mass and explosion energy, which suggests that pre-explosion activity has a strong impact on the structure of the star. This may be important to take into account in future studies of the ability of the neutrino mechanism to explode stars. We also see a possible correlation between the CSM radial extent and ZAMS mass, which could be related to the time with respect to explosion when the CSM is first generated.