A coherent picture for the band structure near the G point and the associated fundamental optical transitions in wurtzite (WZ) GaN, including the electron and hole effective masses and the binding energies of the free excitons associated with different valence bands, has been derived from time-resolved photoluminescence measurements and a theoretical calculation based on the local density approximation. We also determine the radiative recombination lifetimes of the free excitons and neutral impurity (donor and acceptor) bound excitons in WZ GaN and compare ratios of the radiative lifetimes with calculated values of the ratios obtained with existing theories of free and bound excitons.