Context. In this paper we present a grid of self-consistent 1D model atmospheres of cool stars, sub-stellar objects, and exoplanets in the effective temperature range 300-3000 K, including cloud formation, chemical non-equilibrium effects, and stellar irradiation. Aims. The new grid extends the classical MARCS model atmosphere grid from 2008 towards lower effective temperatures and a broader range of object types. Methods. The new model atmosphere computations, MSG, are based on a combination of three well-tested codes, the classical MARCS 1D atmospheres, the StaticWeather cloud formation code, and the GGchem chemical equilibrium code. The combined code has been updated with new and more complete molecular and atomic opacities, cloud formation, and advanced chemical equilibrium calculations, and we also added new numerical methods at low temperatures to allow for a more robust convergence. Results. The coupling between the MARCS radiative transfer and GGchem chemical equilibrium computations has effectively made it possible to reach convergence based on the electron pressure for warmer models and gas pressure for cooler models, enabling self-consistent modelling of stellar, sub-stellar, and exoplanetary objects in a very wide range of effective temperatures. We will make new cloud-free and non-irradiated models for solar metallicity and a selected variety of other chemical compositions immediately available from our home page (https://cels.nbi.ku.dk). Illustrative examples of cloudy and irradiated models as well as models based on non-equilibrium chemistry are also presented, and we will describe these in more detail and make them available upon completion at the same place for a larger range of parameter space. Conclusions. For solar metallicity models, the new additional molecular opacities only affect the structure of models cooler than Teff = 2500 K, and the effect becomes substantial for models below Teff ~1500 K. Atomic line opacities are important for models warmer than ~3000 K. The line profile of the molecular opacities may have a larger effect on the model structure than previously anticipated, particularly in the uppermost layers at low gas pressure. The qualitative changes in the relative abundances of TiO, H2O, CH4, NH3, and other molecules in our models follow the observationally defined M, L, T (and Y) sequences, but they also reveal more complex and depth-dependent abundance changes and therefore a spectral classification depending on more parameters. The self-consistent coupling to StaticWeather cloud computations allows for detailed comparison between nucleation and observed relative dimming of different spectral bands, with advanced applications for new identification methods of potential exoplanetary biology.