We present a very high signal-to-noise ratio composite spectrum created using 657 radio-selected quasars from the FIRST Bright Quasar Survey. The spectrum spans rest-frame wavelengths 900-7500 Å. Additionally, we present composite spectra formed from subsets of the total data set in order to investigate the spectral dependence on radio loudness and the presence of broad absorption lines. In particular, radio-loud quasars are red compared to radio-quiet quasars, and quasars showing low-ionization broad absorption lines are red compared to other quasars. We compare our composites with those from the Large Bright Quasar Survey. Composite quasar spectra have proved to be valuable tools for a host of applications, and in that spirit we make these publicly available via the FIRST survey web page.