The first year of SN 2004dj in NGC 2403

New BV RI photometry and optical spectroscopy of the Type IIp supernova 2004dj in NGC 2403, obtained during the first year since discovery, are presented. The progenitor cluster, Sandage 96, is also detected on pre-explosion frames. The light curve indicates that the explosion occurred about 30 d before discovery, and the plateau phase lasted about +110 +/- 20 d after that. The plateau-phase spectra have been modelled with the SYNOW spectral synthesis code using H, Na I, Ti II, ScII, FeII and Ba I lines. The SN distance is inferred from the expanding photosphere method and the standard candle method applicable for SNe IIp. They resulted in distances that are consistent with each other as well as earlier Cepheid and Tully-Fisher distances. The average distance, D = 3.47 +/- 0.29 Mpc is proposed for SN 2004dj and NGC 2403. The nickel mass produced by the explosion is estimated as similar to 0.02 +/- 0.01 M-circle dot. The spectral energy distribution of the progenitor cluster is reanalysed by fitting population synthesis models to our observed BV RI data supplemented by U and JHK magnitudes from the literature. The chi(2) minimization revealed a possible 'young' solution with cluster age T-cl = 8 Myr, and an 'old' solution with T-cl = 20-30 Myr. The 'young' solution would imply a progenitor mass M > 20 M-circle dot, which is higher than the previously detected progenitor masses for Type II SNe.