AU Microscopii's debris disc is one of the most famous and best-studied debris discs and one of only two resolved debris discs around M stars. We perform in-depth collisional modelling of the AU Mic disc including stellar radiative and corpuscular forces (stellar winds), aiming at a comprehensive understanding of the dust production and the dust and planetesimal dynamics in the system. Our models are compared to a suite of observational data for thermal and scattered light emission, ranging from the ALMA radial surface brightness profile at 1.3 mm to spatially resolved polarisation measurements in the visible. Most of the data are shown to be reproduced with dust production in a belt of planetesimals with an outer edge at around 40 au and subsequent inward transport of dust by stellar winds. A low dynamical excitation of the planetesimals with eccentricities up to 0 : 03 is preferred. The radial width of the planetesimal belt cannot be constrained tightly. Belts that are 5 au and 17 au wide, as well as a broad 44 au-wide belt, are consistent with observations. All models show surface density profiles that increase with distance from the star up to approximate to 40 au, as inferred from observations. The best model is achieved by assuming a stellar mass loss rate that exceeds the solar one by a factor of 50. The models reproduce the spectral energy distribution and the shape of the ALMA radial profile well, but deviate from the scattered light observations more strongly. The observations show a bluer disc colour and a lower degree of polarisation for projected distances <40 au than predicted by the models. These deviations may be reduced by taking irregularly shaped dust grains which have scattering properties different from the Mie spheres used in this work. From tests with a handful of selected dust materials, we favour mixtures of silicate, carbon, and ice of moderate porosity. We also address the origin of the unresolved central excess emission detected by ALMA and show that it cannot stem from an additional inner belt alone. Instead, it should derive, at least partly, from the chromosphere of the central star.