  NGC 3532 is an extremely rich open cluster embedded in the Galactic disc,
hitherto lacking a comprehensive, documented membership list. We provide
membership probabilities from new radial velocity observations of solar-type
and low-mass stars in NGC 3532, in part as a prelude to a subsequent study of
stellar rotation in the cluster. Using extant optical and infra-red photometry
we constructed a preliminary photometric membership catalogue, consisting of
2230 dwarf and turn-off stars. We selected 1060 of these for observation with
the AAOmega spectrograph at the Anglo-Australian Telescope and 391 stars for
observations with the Hydra-South spectrograph at the Victor Blanco Telescope,
obtaining spectroscopic observations over a decade for 145 stars. We measured
radial velocities for our targets through cross-correlation with model spectra
and standard stars, and supplemented them with radial velocities for 433
additional stars from the literature. We also measured log g, Teff, and [Fe/H]
from the AAOmega spectra. Together with proper motions from Gaia DR2 we find
660 exclusive members. The members are distributed across the whole cluster
sequence, from giant stars to M dwarfs, making NGC 3532 one of the richest
Galactic open clusters known to date, on par with the Pleiades. From further
spectroscopic analysis of 153 dwarf members we find the metallicity to be
marginally sub-solar, with [Fe/H]=-0.07. Exploiting trigonometric parallax
measurements from Gaia DR2 we find a distance of $484^{+35}_{-30}$ pc. Based on
the membership we provide an empirical cluster sequence in multiple photometric
passbands. A comparison of the photometry of the measured cluster members with
several recent model isochrones enables us to confirm the 300 Myr cluster age.
However, all of the models evince departures from the cluster sequence in
particular regions, especially in the lower mass range. (abridged)
