We have used the VLA FIRST survey and the APM catalog of the POSS-I plates as the basis for constructing a new radio-selected sample of optically bright quasars. This is the first radio-selected sample that is competitive in size with current optically selected quasar surveys. Using only two basic criteria, radio-optical positional coincidence and optical morphology, quasars and BL Lacs can be identified with 60% selection efficiency; the efficiency increases to 70% for objects fainter than magnitude 17. We show that a more sophisticated selection scheme can predict with better than 85% reliability which candidates will turn out to be quasars. This paper presents the second installment of the FIRST Bright Quasar Survey with a catalog of 636 quasars distributed over 2682 square degrees. The quasar sample is characterized and all spectra are displayed. The FBQS detects both radio-loud and radio-quiet quasars out to a redshift z>3. We find a large population of objects of intermediate radio-loudness; there is no evidence in our sample for a bimodal distribution of radio characteristics. The sample includes ~29 broad absorption line quasars, both high and low ionization, and a number of new objects with remarkable optical spectra.
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