This is the accepted manuscript version of an article accepted for publication in Monthly Notices of the Royal Astronomical Society following peer review. The version of record, P. De Vis et al; ???Herschel ??? ATLAS: revealing dust build-up and decline across gas, dust and stellar mass selected samples ??? I. Scaling relations???, MNRAS (2016), 464(4): 4680-4705, first published online October 19, 2016, is available online via doi: https://doi.org/10.1093/mnras/stw2501 Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved ; We present a study of the dust, stars and atomic gas (HI) in an HI-selected sample of local galaxies (z 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 fraction (proxy for evolutionary state of a galaxy). The most robust scaling relations for gas and dust are those linked to NUV-r (SSFR) and gas fraction, these do not depend on sample selection or environment. At the highest gas fractions, our additional sample shows 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 timescale. We link this trend to the changing efficiency of conversion of HI to H2 as galaxies increase in stellar mass surface density as they evolve. 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.