ABSTRACT We present Atacama Large Millimetre Array observations of a small but statistically complete sample of 12 250-μm-selected galaxies at z = 0.35 designed to measure their dust submillimeter continuum emission as well as their $\rm {^{12}CO(1-0)}$ and atomic carbon [C i](3P1−3P0) spectral lines. This is the first sample of galaxies with global measures of all three H2-mass tracers and that shows star formation rates (4–26 $\rm M_{\odot}$ yr−1) and infrared luminosities ($1\!-\!6\times 10^{11}\,\rm L_{\odot}$) typical of star-forming galaxies in their era. We find a surprising diversity of morphology and kinematic structure; one third of the sample have evidence for interaction with nearby smaller galaxies, several sources have disjoint dust and gas morphology. Moreover, two galaxies have very high $L^{\prime }_{\rm C\,{\small I}}$ / $L^{\prime }_{\rm {CO}}$ ratios for their global molecular gas reservoirs; if confirmed, such extreme intensity ratios in a sample of dust-selected, massive star-forming galaxies present a challenge to our understanding of interstellar medium. Finally, we use the emission of the three molecular gas tracers, to determine the carbon abundance, $\rm {X_{C\,{\small I}}}$ , and CO–$\rm {H_2}$ conversion αCO in our sample, using a weak prior that the gas-to-dust ratio is similar to that of the Milky Way for these massive and metal-rich galaxies. Using a likelihood method that simultaneously uses all three gas tracer measurements, we find mean values and errors on the mean of $\langle\alpha _{\rm {CO}}\rangle = 3.0\pm 0.5\, \rm {M}_{\odot }\, (\rm{K}\, \rm{kms}^{-1}\, \rm{pc}^2)^{-1}$ and $\langle \rm{X}_{\rm{CI}} \rangle =1.6\pm 0.1\times 10^{-5}$ (or $\alpha _{\rm{CI}} = 18.8\,\rm {M}_{\odot }\, (\rm{K}\, \rm{kms}^{-1}\, \rm{pc}^2)^{-1}$) and $\delta _{\rm {GDR}} = 128\pm 16$ (or $\alpha _{850} = 5.9\times 10^{12}\, \rm {W}\, \rm{Hz}^{-1}\,\rm {M}_{\odot }\,^{-1}$), where our starting assumption is that these metal-rich galaxies have an average gas-to-dust ratio similar to that of the Milky Way centred on $\rm{\delta} _{\rm {GDR}} =135$.