We present some first results on the variability, polarization and general properties of radio sources selected at 20 GHz, the highest frequency at which a sensitive radio survey has been carried out over a large area of sky. Sources with flux densities above 100 mJy in the Australia Telescope Compact Array 20 GHz pilot survey at declination -60 degrees to -70 degrees were observed at up to three epochs during 2002-04, including near-simultaneous measurements at 5, 8 and 18 GHz in 2003. Of the 173 sources detected, 65 per cent are candidate QSOs or BL Lac objects, 20 per cent galaxies and 15 per cent faint (b(J) > 22 mag) optical objects or blank fields.On a 1-2 yr time-scale, the general level of variability at 20 GHz appears to be low. For the 108 sources with good-quality measurements in both 2003 and 2004, the median variability index at 20 GHz was 6.9 per cent and only five sources varied by more than 30 per cent in flux density.Most sources in our sample show low levels of linear polarization (typically 1-5 per cent), with a median fractional polarization of 2.3 per cent at 20 GHz. There is a trend for fainter 20 GHz sources to have higher fractional polarization.At least 40 per cent of sources selected at 20 GHz have strong spectral curvature over the frequency range 1-20 GHz. We use a radio 'two-colour diagram' to characterize the radio spectra of our sample, and confirm that the flux densities of radio sources at 20 GHz (which are also the foreground point-source population for cosmic microwave background anisotropy experiments like Wilkinson Microwave Anisotropy Probe and Planck) cannot be reliably predicted by extrapolating from surveys at lower frequencies. As a result, direct selection at 20 GHz appears to be a more efficient way of identifying 90 GHz phase calibrators for Atacama Large Millimeter Array (ALMA) than the currently proposed technique of extrapolation from radio surveys at 1-5 GHz.