We present a statistical study of interplanetary conditions and geospace response to 89 coronal mass ejection-driven sheaths observed during Solar Cycles 23 and 24. We investigate in particular the dependencies on the driver properties and variations across the sheath. We find that the ejecta speed principally controls the sheath geoeffectiveness and shows the highest correlations with sheath parameters, in particular in the region closest to the shock. Sheaths of fast ejecta have on average high solar wind speeds, magnetic (B) field magnitudes, and fluctuations, and they generate efficiently strong out-of-ecliptic fields. Slow-ejecta sheaths are considerably slower and have weaker fields and field fluctuations, and therefore they cause primarily moderate geospace activity. Sheaths of weak and strong B field ejecta have distinct properties, but differences in their geoeffectiveness are less drastic. Sheaths of fast and strong ejecta push the subsolar magnetopause significantly earthward, often even beyond geostationary orbit. Slow-ejecta sheaths also compress the magnetopause significantly due to their large densities that are likely a result of their relatively long propagation times and source near the streamer belt. We find the regions near the shock and ejecta leading edge to be the most geoeffective parts of the sheath. These regions are also associated with the largest B field magnitudes, out-of-ecliptic fields, and field fluctuations as well as largest speeds and densities. The variations, however, depend on driver properties. Forecasting sheath properties is challenging due to their variable nature, but the dependence on ejecta properties determined in this work could help to estimate sheath geoeffectiveness through remote-sensing coronal mass ejection observations.