We present a catalogue of 1602 white-dwarf-main-sequence (WDMS) binaries from the spectroscopic Sloan Digital Sky Survey Data Release 6 (SDSS DR6). Among these, we identify 440 as new WDMS binaries. We select WDMS binary candidates by template fitting all 1.27 million DR6 spectra, using combined constraints in both chi 2 and signal-to-noise ratio. In addition, we use Galaxy Evolution Explorer (GALEX) and UKIRT Infrared Sky Survey (UKIDSS) magnitudes to search for objects in which one of the two components dominates the SDSS spectrum. We use a decomposition/fitting technique to measure the effective temperatures, surface gravities, masses and distances to the white dwarfs, as well as the spectral types and distances to the companions in our catalogue. Distributions and density maps obtained from these stellar parameters are then used to study both the general properties and the selection effects of WDMS binaries in the SDSS. A comparison between the distances measured to the white dwarfs and the main-sequence companions shows d(sec) > d(wd) for approximately one-fifth of the systems, a tendency already found in our previous work. The hypothesis that magnetic activity raises the temperature of the inter-spot regions in active stars that are heavily covered by cool spots, leading to a bluer optical colour compared to inactive stars, remains the best explanation for this behaviour. We also make use of SDSS-GALEX-UKIDSS magnitudes to investigate the distribution of WDMS binaries, as well as their white-dwarf effective temperatures and companion star spectral types, in ultraviolet to infrared colour space. We show that WDMS binaries can be very efficiently separated from single main-sequence stars and white dwarfs when using a combined ultraviolet, optical and infrared colour selection. Finally, we also provide radial velocities for 1068 systems measured from the Na i lambda lambda 8183.27, 8194.81 absorption doublet and/or the H alpha emission line. Among the systems with multiple SDSS spectroscopy, we find five new systems exhibiting significant radial velocity variations, identifying them as post-common-envelope binary candidates.