[en] We perform spherically symmetric general-relativistic simulations of core collapse and the postbounce pre-explosion phase in 32 presupernova stellar models of solar metallicity with zero-age main-sequence masses of 12-120 M _☉. Using energy-dependent three-species neutrino transport in the two-moment approximation with an analytic closure, we show that the emitted neutrino luminosities and spectra follow very systematic trends that are correlated with the compactness (∼M/R) of the progenitor star's inner regions via the accretion rate in the pre-explosion phase. We find that these qualitative trends depend only weakly on the nuclear equation of state (EOS), but quantitative observational statements will require independent constraints on the EOS and the rotation rate of the core as well as a more complete understanding of neutrino oscillations. We investigate the simulated response of water Cherenkov detectors to the electron antineutrino fluxes from our models and find that the large statistics of a galactic core collapse event may allow robust conclusions on the inner structure of the progenitor star.