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The Australia Telescope 20 GHz (AT20G) survey is a blind survey of the whole Southern sky at 20 GHz with follow-up observations at 4.8, 8.6 and 20 GHz carried out with the Australia Telescope Compact Array (ATCA) from 2004 to 2008. In this paper we present an analysis of radio spectral properties in total intensity and polarization, sizes, optical identifications and redshifts of the sample of the 5808 extragalactic sources in the survey catalogue of confirmed sources over 6.1 sr in the Southern sky (i.e. the whole Southern sky excluding the strip at Galactic latitude | b| < ). The sample has a flux density limit of 40 mJy. Completeness has been measured as a function of scan region and flux density. Averaging over the whole survey area the follow-up survey is 78 per cent complete above 50 mJy and 93 per cent complete above 100 mJy. 3332 sources with declination have good quality almost simultaneous observations at 4.8, 8.6 and 20 GHz. The spectral analysis shows that the sample is dominated by flat-spectrum sources, with 69 per cent having spectral index . The fraction of flat-spectrum sources decreases from 81 per cent for mJy to 60 per cent for mJy. There is also a clear spectral steepening at higher frequencies with the median decreasing from between 4.8 and 8.6 GHz to between 8.6 and 20 GHz. Simultaneous observations in polarization are available for all the sources at all the frequencies. 768 sources have a good-quality detection of polarized flux density at 20 GHz; 467 of them were also detected in polarization at 4.8 and/or at 8.6 GHz so that it has been possible to compare the spectral behaviour in total intensity and polarization. We have found that the polarized fraction increases slightly with frequency and decreases with flux density. The spectral indices in total intensity and in polarization are, on average, close to each other, but we also found several sources for which the spectral shape of the polarized emission is substantially different from the spectral shape in total intensity. The correlation between the spectral indices in total intensity and in polarization is weaker for flat-spectrum sources. Cross-matches and comparisons have been made with other catalogues at lower radio frequencies, and in the optical, X-ray and -ray bands. Redshift estimates are available for 825 sources. [ABSTRACT FROM AUTHOR]