We present the results of a systematic study of 150 gamma-ray bursts (GRBs) with reliable redshift estimates detected in the triggered mode of the Konus-Wind (KW) experiment. The sample covers the period from 1997 February to 2016 June and represents the largest set of cosmological GRBs studied to date over a broad energy band. We provide the burst durations, the spectral lags, the results of spectral fits with two model functions, the total energy fluences, and the peak energy fluxes, the rest-frame, isotropic-equivalent energy and peak luminosity, and the collimation-corrected values of the energetics for 32 GRBs with reasonably-constrained jet breaks. We consider the behavior of the rest-frame GRB parameters in the hardness-duration and hardness-intensity planes, and confirm the "Amati" and "Yonetoku" relations for Type II GRBs. The correction for the jet collimation does not improve these correlations for the KW sample. We discuss the influence of instrumental selection effects on the GRB parameter distributions and estimate the KW GRB detection horizon. Accounting for the instrumental bias, we estimate the KW GRB luminosity evolution, luminosity and isotropic-energy functions, and the evolution of the GRB formation rate.