We present details of a new sample of radio-loud quasars drawn from 0.013 sr of the 7C Redshift Survey. This sample is small (21 quasars) but complete in that every object with an unresolved nucleus and/or broad emission lines with S(151MHz) > 0.5 Jy has been discovered. The dependence of the quasar fraction with redshift and radio luminosity is investigated, providing new evidence supporting the unification of radio-loud quasars and powerful radio galaxies. This 7C sample is compared with optically-selected quasars, in order to determine whether there are systematic biases in the different selection techniques. There are no lightly reddened (Av approx. 1) quasars in our sample amongst the 14 with z < 2. The discovery of a reddened quasar at z = 2.034 and its implications are discussed. A tight correlation between radio luminosity and optical/near infrared continuum luminosity for a subset of the sample is also found.