Aims. We aim to present simulated chemical abundance profiles for a variety of important species, with special attention given to spin-state chemistry, in order to provide reference results against which present and future models can be compared. Methods. We employ gas-phase and gas-grain models to investigate chemical abundances in physical conditions corresponding to starless cores. To this end, we have developed new chemical reaction sets for both gas-phase and grain-surface chemistry, including the deuterated forms of species with up to six atoms and the spin-state chemistry of light ions and of the species involved in the ammonia and water formation networks. The physical model is kept simple in order to facilitate straightforward benchmarking of other models against the results of this paper. Results. We find that the ortho/para ratios of ammonia and water are similar in both gas-phase and gas-grain models, at late times in particular, implying that the ratios are determined by gas-phase processes. We derive late-time ortho/para ratios of ~0.5 and ~1.6 for ammonia and water, respectively. We find that including or excluding deuterium in the calculations has little effect on the abundances of non-deuterated species and on the ortho/para ratios of ammonia and water, especially in gas-phase models where deuteration is naturally hindered owing to the presence of abundant heavy elements. Although we study a rather narrow temperature range (10-20 K), we find strong temperature dependence in, e.g., deuteration and nitrogen chemistry. For example, the depletion timescale of ammonia is significantly reduced when the temperature is increased from 10 to 20 K; this is because the increase in temperature translates into increased accretion rates, while the very high binding energy of ammonia prevents it from being desorbed at 20 K.