We report a first-principles study of the superconducting critical temperature and other properties of Fe-based superconductors taking into account, on equal footing, phonon, charge, and spin-fluctuation mediated Cooper pairing. We show that in FeSe this leads to a modulated s ± gap symmetry and that the antiferromagnetic paramagnons are the leading mechanism for superconductivity in FeSe, overcoming the strong repulsive effect of both phonons and charge pairing.