Background: r-process nucleosynthesis models rely, by necessity, on nuclear structure models for input. Particularly important are β-decay half-lives of neutron-rich nuclei. At present only a single systematic calculation exists that provides values for all relevant nuclei making it difficult to test the sensitivity of nucleosynthesis models to this input. Additionally, even though there are indications that their contribution may be significant, the impact of first-forbidden transitions on decay rates has not been systematically studied within a consistent model. Purpose: Our goal is to provide a table of β-decay half-lives and β-delayed neutron emission probabilities, including first-forbidden transitions, calculated within a fully self-consistent microscopic theoretical framework. The results are used in an r-process nucleosynthesis calculation to asses the sensitivity of heavy element nucleosynthesis to weak interaction reaction rates. Method: We use a fully self-consistent covariant density functional theory (CDFT) framework. The ground state of all nuclei is calculated with the relativistic Hartree-Bogoliubov (RHB) model, and excited states are obtained within the proton-neutron relativistic quasiparticle random phase approximation (pn-RQRPA). Results: The β-decay half-lives, β-delayed neutron emission probabilities, and the average number of emitted neutrons have been calculated for 5409 nuclei in the neutron-rich region of the nuclear chart. We observe a significant contribution of the first-forbidden transitions to the total decay rate in nuclei far from the valley of stability. The experimental half-lives are in general well reproduced for even-even, odd-A, and odd-odd nuclei, in particular for short-lived nuclei. The resulting data table is included with the article as Supplemental Material. Conclusions: In certain regions of the nuclear chart, first-forbidden transitions constitute a large fraction of the total decay rate and must be taken into account consistently in modern evaluations of half-lives. Both the β-decay half-lives and β-delayed neutron emission probabilities have a noticeable impact on the results of heavy element nucleosynthesis models.