The physics of active super massive black holes (BHs) is governed by their mass (M_BH), spin (a_*), and accretion rate (M). This work is the first in a series of papers with the aim of testing how these parameters determine the observable attributes of active galactic nuclei (AGN). We have selected a sample in a narrow redshift range, centred on z similar to 1.55, that covers a wide range in M_BH and M, and are observing them with X-shooter, covering rest wavelengths similar to 1200-9800 A. The current work covers 30 such objects and focuses on the origin of the AGN spectral energy distribution (SED). After estimating M_BH and M based on each observed SED, we use thin accretion disc (AD) models and a Bayesian analysis to fit the observed SEDs in our sample. We are able to fit 22/30 of the SEDs. Out of the remaining eight SEDs, three can be fit by the thin AD model by correcting the observed SED for reddening within the host galaxy and four can be fit by adding a disc wind to the model. In four of these eight sources, Milky Way-type extinction, with the strong 2175 A feature, provides the best reddening correction. The distribution in spin parameter covers the entire range, from -1 to 0.998, and the most massive BHs have spin parameters greater than 0.7. This is consistent with the 'spin-up' model of BH evolution. Altogether, these results indicate that thin ADs are indeed the main power houses of AGN, and earlier claims to the contrary are likely affected by variability and a limited observed wavelength range.