A survey of the entire southern sky for millisecond and low-luminosity pulsars using the ATNF Parkes radio telescope has now been completed. The survey detected 298 pulsars, of which 101 were previously unknown. The new pulsars include 17 millisecond pulsars. This is the largest sample of both normal and millisecond pulsars detected in any survey. Combining our sample with other recent surveys in the Northern Hemisphere, we present a statistical study of the populations of both normal and millisecond pulsars. We find that the improved statistics allow us to estimate the number and birth-rate of both types of pulsar down to a 400-MHz luminosity limit of 1 mJy kpc^2. The local surface densities of potentially observable normal pulsars and millisecond pulsars are both about 30 kpc^-2, corresponding to ~30000 potentially observable pulsars of each type in the Galaxy. Once beaming effects are taken into consideration we estimate that the active population of normal pulsars is ~160000. Although there is evidence for flattening of the luminosity function of normal pulsars, this is not evident for millisecond pulsars which probably have a substantial population with luminosities below 1 mJy kpc^2. After correcting for beaming effects, we estimate that a normal pulsar is born with a luminosity greater than 1 mJy kpc^2 between once every 60 and 330 yr in the Galaxy. The birth-rate of millisecond pulsars is at least 3x10^-6 yr^-1 above the same luminosity limit. Modelling the observed transverse speeds of millisecond pulsars using a dynamical simulation, we find their mean birth velocity to be 130+/-30 km s^-1, significantly lower than that of the normal pulsars.