In a previous paper we showed that the radio sources selected by combining large area radio and optical surveys, have a strong deficit of radio emission with respect to 3CR radio-galaxies matched in line emission luminosity. We argued that the prevalence of sources with luminous extended radio structures in high flux-limited samples is due to a selection bias. Sources with low radio power form the bulk of the radio-loud AGN population but are still virtually unexplored. We here analyze their photometric and spectroscopic properties. From the point of view of their emission lines, the majority of the sample are Low Excitation Galaxies (LEG), similar to the 3CR objects at the same level of line luminosity. The hosts of the LEG are red, massive (10.5 less than or similar to log M(*)/M(circle dot) less than or similar to 12) Early-Type Galaxies (ETG) with large black hole masses (7.7 less than or similar to log M(BH)/M(circle dot) less than or similar to 9), statistically indistinguishable from the hosts of low redshift 3CR/LEG sources. No genuine radio-loud LEG could be found associated with black holes with a mass substantially smaller than 10(8) M(circle dot) or with a late type host. The fraction of galaxies with signs of star formation (similar to 5%) is similar to what is found in both the quiescent ETG and 3CR/LEG hosts. We conclude that the deficit in radio emission cannot be ascribed to differences in the properties of their hosts. We argue that instead this could be due to a temporal evolution of the radio luminosity. A minority (similar to 10%) of the sample show rather different properties; these are associated with low black hole masses, with spiral galaxies, or with a high excitation spectrum. In general these outliers are the result of the contamination from Seyfert galaxies and from those where the radio emission is powered by star formation. For the objects with high excitation spectra there is no clear discontinuity in either the host or nuclear properties because they include radio-quiet as well as radio-loud AGN.