We present a new analysis of the potential power of deep, near-infrared, imaging surveys with the James Webb Space Telescope (JWST) to improve our knowledge of galaxy evolution. In this work we properly simulate what can be achieved with realistic survey strategies, and utilise rigorous signal:noise calculations to calculate the resulting posterior constraints on the physical properties of galaxies. We explore a broad range of assumed input galaxy types (>20,000 models, including extremely dusty objects) across a wide redshift range (out to z~12), while at the same time considering a realistic mix of galaxy properties based on our current knowledge of the evolving population (as quantified through the Empirical Galaxy Generator: EGG). While our main focus is on imaging surveys with NIRCam, spanning lambda(obs) = 0.6-5.0 microns, an important goal of this work is to quantify the impact/added-value of: i) parallel imaging observations with MIRI at longer wavelengths, and ii) deeper supporting optical/UV imaging with HST (potentially prior to JWST launch) in maximising the power and robustness of a major extragalactic NIRCam survey. We show that MIRI parallel 7.7-micron imaging is of most value for better constraining the redshifts and stellar masses of the dustiest (A_V > 3) galaxies, while deep B-band imaging (reaching~28.5 AB mag) with ACS on HST is vital for determining the redshifts of the large numbers of faint/low-mass, z <5 galaxies that will be detected in a deep JWST NIRCam survey.