We present the first simultaneous photometric and spectroscopic investigation of a large set of RR Lyrae variables in a globular cluster. The radial-velocity (RV) data presented comprise the largest sample of RVs of RR Lyrae stars ever obtained. The target is M3; BVIC time series of 111 and b flux data of further 64 RRab stars and RV data of 79 RR Lyrae stars are published. Blazhko modulation of the light curves of 47 per cent of the RRab stars is detected. The mean value of the centre-of-mass velocities of RR Lyrae stars is -146.8 km s-(1) with 4.52 km s(-1) standard deviation, which is in good agreement with the results obtained for the red giants of the cluster. The Phi(RV)(21) phase difference of the RV curves of RRab stars is found to be uniformly constant both for theM3 and for Galactic field RRab stars; no period or metallicity dependence of the Phi(RV)(21) is detected. The Baade-Wesselink distances of 26 non-Blazhko variables with the best phase-coverage RV curves are determined; the corresponding distance of the cluster, 10 480 +/- 210 pc, agrees with the previous literature information. A quadratic formula for the A(puls) - A(V) relation of RRab stars is given, which is valid for both OoI and OoII variables. We also show that (V - I)(0) of RRab stars measured at light minimum is period dependent; there is at least 0.1 mag difference between the colours at minimum light of the shortest and longest period variables.