We present observations of the stellar and gas kinematics for a representative sample of 24 Sa galaxies obtained with our custom-built integral-field spectrograph SAURON operating on the William Herschel Telescope. The data have been homogeneously reduced and analysed by means of a dedicated pipeline. All resulting data cubes were spatially binned to a minimum mean signal-to-noise ratio of 60 per spatial and spectral resolution element. Our maps typically cover the bulge-dominated region. We find a significant fraction of kinematically decoupled components (12/24), many of them displaying central velocity dispersion minima. They are mostly aligned and co-rotating with the main body of the galaxies, and are usually associated with dust discs and rings detected in unsharp-masked images. Almost all the galaxies in the sample (22/24) contain significant amounts of ionized gas which, in general, is accompanied by the presence of dust. The kinematics of the ionized gas are consistent with circular rotation in a disc co-rotating with respect to the stars. The distribution of mean misalignments between the stellar and gaseous angular momenta in the sample suggests that the gas has an internal origin. The [OIII]/Hβ ratio is usually very low, indicative of current star formation, and shows various morphologies (ring-like structures, alignments with dust lanes or amorphous shapes). The star formation rates (SFRs) in the sample are comparable with that of normal disc galaxies. Low gas velocity dispersion values appear to be linked to regions of intense star formation activity. We interpret this result as stars being formed from dynamically cold gas in those regions. In the case of NGC5953, the data suggest that we are witnessing the formation of a kinematically decoupled component from cold gas being acquired during the ongoing interaction with NGC5954.