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The Galactic centre black hole candidate Sgr A* is the best target for studies of low-luminosity accretion physics, including with near-infrared (NIR) and submillimetre wavelength long baseline interferometry experiments. Here, we compare images and spectra generated from a parameter survey of general relativistic MHD simulations to a set of radio to NIR observations of Sgr A*. Our models span the limits of weak and strong magnetization and use a range of sub-grid prescriptions for electron heating. We find two classes of scenarios can explain the broad shape of the submillimetre spectral peak and the highly variable NIR flaring emission. Weakly magnetized 'disc-jet' models where most of the emission is produced near the jet wall, consistent with past work, as well as strongly magnetized (magnetically arrested disc) models where hot electrons are present everywhere. Disc-jet models are strongly depolarized at submillimetre wavelengths as a result of strong Faraday rotation, inconsistent with observations of Sgr A*. We instead favour the strongly magnetized models, which provide a good description of the median and highly variable linear polarization signal. The same models can also explain the observed mean Faraday rotation measure and potentially the polarization signals seen recently in Sgr A* NIR flares. [ABSTRACT FROM AUTHOR]