The prospect of detecting the first galaxies by observing their impact on the intergalactic medium (IGM) as they reionized it during the first billion years leads us to ask whether such indirect observations are capable of diagnosing which types of galaxies were most responsible for reionization. We attempt to answer this with new large-scale radiative transfer simulations of reionization including the entire mass range of atomically cooling haloes (M > 108 M⊙). We divide these haloes into two groups, high-mass, atomically cooling haloes, or HMACHs (M > 109 M⊙), and low-mass, atomically cooling haloes, or LMACHs (108 < M < 109 M⊙), the latter being susceptible to negative feedback due to Jeans mass filtering in ionized regions, which leads to a process we refer to as self-regulation. We focus here on predictions of the redshifted 21-cm emission, to see if upcoming observations are capable of distinguishing a universe ionized primarily by HMACHs from one in which both HMACHs and LMACHs are responsible, and to see how these results depend upon the uncertain source efficiencies. We find that 21-cm fluctuation power spectra observed by the first-generation Epoch of Reionization 21-cm radio interferometer arrays should be able to distinguish the case of reionization by HMACHs alone from that by both HMACHs and LMACHs, together. Some reionization scenarios, e.g. one with abundant low-efficiency sources versus one with self-regulation, yield very similar power spectra and rms evolution and thus can only be discriminated by their different mean reionization history and 21-cm probability distribution function (PDF) distributions. We also find that the skewness of the 21-cm PDF distribution smoothed with Low Frequency Array (LOFAR)-like resolution shows a clear feature correlated with the rise of the rms due to patchiness. This is independent of the reionization scenario and thus provides a new approach for detecting the rise of large-scale patchiness. The peak epoch of the 21-cm rms fluctuations depends significantly on the beam and bandwidth smoothing size as well as on the reionization scenario and can occur for ionized fractions as low as 30 per cent and as high as 70 per cent. Measurements of the mean photoionization rates are sensitive to the average density of the regions being studied and therefore could be strongly skewed in certain cases. Finally, the simulation volume employed has very modest effects on the results during the early and intermediate stages of reionization, but late-time signatures could be significantly affected.