  We define a complete sample of thirty-three GHz-Peaked-Spectrum (GPS) radio
sources based on their spectral properties. We present measurements of the
radio spectra and polarization of the complete sample and a list of additional
GPS sources which fail one or more criteria to be included in the complete
sample. The majority of the data have been obtained from quasi-simultaneous
multi-frequency observations at the Very Large Array (VLA) during 3 observing
sessions. Low frequency data from the Westerbork Synthesis Radio Telescope
(WSRT) and from the literature have been combined with the VLA data in order to
better define the spectral shape.
  The objects presented here show a rather wide range of spectral indices at
high and low frequencies, including a few cases where the spectral index below
the turnover is close to the theoretical value of 2.5 typical of self-absorbed
incoherent synchrotron emission. Faint and diffuse extended emission is found
in about 10% of the sources. In the majority of the GPS sources, the fractional
polarization is found to be very low, consistent with the residual instrumental
polarization of 0.3%.
