We present a study of the dust, stars and atomic gas (HI) in an HI-selected sample of local galaxies (z < 0.035) in the Herschel Astrophysical Terahertz Large Area Survey fields. This HI-selected sample reveals a population of very high gas fraction (> 80 per cent), low stellar mass sources that appear to be in the earliest stages of their evolution.We compare this sample with dust- and stellar-mass-selected samples to study the dust and gas scaling relations over a wide range of gas fractions (proxy for evolutionary state of a galaxy). The most robust scaling relations for gas and dust are those linked to near-ultraviolet - r (specific star formation rate) and gas fraction; these do not depend on sample selection or environment. At the highest gas fractions, our additional sample shows that the dust content is well below expectations from extrapolating scaling relations for more evolved sources, and dust is not a good tracer of the gas content. The specific dust mass for local galaxies peaks at a gas fraction of ~75 per cent. The atomic gas depletion time is also longer for high gas fraction galaxies, opposite to the trend found for molecular gas depletion time-scale. We link this trend to the changing efficiency of conversion of HI to H2 as galaxies increase in stellar mass surface density during their evolution. Finally, we show that galaxies start out barely obscured and increase in obscuration as they evolve, yet there is no clear and simple link between obscuration and global galaxy properties.