The Planck-ATCA Co-eval Observations (PACO) project has yielded observations of 464 sources with the Australia Telescope Compact Array (ATCA) between 4.5 and 40GHz. The main purpose of the project was to investigate the spectral properties of mm-selected radio sources at frequencies below and overlapping with the ESA's Planck satellite frequency bands, minimizing the variability effects by observing almost simultaneously with the first two Planck all-sky surveys. In this paper we present the whole catalogue of observations in total intensity. By comparing PACO with the various measures of Planck Catalog of Compact Sources (PCCS) flux densities we found the best consistency with the PCCS 'detection pipeline' photometry (DETFLUX) that we used to investigate the spectral properties of sources from 5 to 217GHz. Of our sources, 91 percent have remarkably smooth spectrum, well described by a double power-law over the full range. This suggests a single emitting region, at variance with the notion that `flat' spectra result from the superposition of the emissions from different compact regions, self-absorbed up to different frequencies. Most of the objects show a spectral steepening above =~30GHz, consistent with synchrotron emission becoming optically thin. Thus, the classical dichotomy between flat-spectrum/compact and steep-spectrum/extended radio sources, well established at cm wavelengths, breaks down at mm wavelengths. The mm-wave spectra do not show indications of the spectral break expected as the effect of `electron ageing', suggesting young source ages.