  Interferometry of the cosmic 21-cm signal is set to revolutionise our
understanding of the Epoch of Reionisation (EoR) and the Cosmic Dawn (CD). The
culmination of ongoing efforts will be the upcoming Square Kilometre Array
(SKA), which will provide tomography of the 21-cm signal from the first billion
years of our Universe. Using a galaxy formation model informed by high-$z$
luminosity functions, here we forecast the accuracy with which the first phase
of SKA-low (SKA1-low) can constrain the properties of the unseen galaxies
driving the astrophysics of the EoR and CD. We consider three observing
strategies: (i) deep (1000h on a single field); (ii) medium-deep (100hr on 10
independent fields); and (iii) shallow (10hr on 100 independent fields). Using
the 21-cm power spectrum as a summary statistic, and conservatively only using
the 21-cm signal above the foreground wedge, we predict that all three
observing strategies should recover astrophysical parameters to a fractional
precision of $\sim 0.1$ -- 10 per cent. The reionisation history is recovered
to an uncertainty of $\Delta z \lesssim 0.1$ (1$\sigma$) for the bulk of its
duration. The medium-deep strategy, balancing thermal noise against cosmic
variance, results in the tightest constraints, slightly outperforming the deep
strategy. The shallow observational strategy performs the worst, with up to a
$\sim 10$ -- 60 per cent increase in the recovered uncertainty. We note,
however, that non-Gaussian summary statistics, tomography, as well as unbiased
foreground removal would likely favour the deep strategy.
