This is the second paper in a series studying the photometric and spectroscopic properties of galaxies of different luminosities in the Coma cluster . We present the sample selection , spectroscopic observations and completeness functions . To study the spectral properties of galaxies as a function of their local environment , two fields were selected for spectroscopic observations to cover both the core ( Coma1 ) and outskirts ( ie . south-west of the core and centered on NGC4839 ) - ( Coma3 ) of the cluster . To maximise the efficiency of spectroscopic observations , two sub-samples were defined , consisting of ‘ bright ’ and ‘ faint ’ galaxies , both drawn from magnitude-limited parent samples . Medium resolution spectroscopy ( 6-9 Å ) was then carried out for a total of 490 galaxies in both fields ( 302 in Coma1 and 188 in Coma3 ) , using the WYFFOS multi-fiber spectrograph on the William Herschel Telescope . The galaxies cover a range of 12 < R < 20 , corresponding to -23 < M _ { R } < -15 ( H _ { 0 } = 65 km/sec/Mpc . The redshifts for these galaxies are measured with an accuracy of 100 km/sec . The spectral line strengths and equivalent widths are also measured for the same galaxies and analysed in Poggianti et al ( 2001- paper III ) . A total of 189 ( Coma1 ) and 90 ( Coma3 ) galaxies are identified as members of the Coma cluster . An analysis of the colors show that only two members of the Coma cluster in our sample have B - R > 2 . The completeness functions for our sample are calculated . These show that the ‘ bright sample ’ is 65 \% complete at R < 17 mag , becoming increasingly incomplete towards fainter magnitudes , while the ‘ faint sample ’ follows a monotonically decreasing completeness function at R > 19 mag .