Analysis of recent photometric observations of the W Vir star ST Pup reveals that it has experienced one sudden period change in the last 35 years. This is in sharp contrast to its erratic behaviour in the first half of this century when the period changed much more frequently. Application of the surface brightness version of the Baade-Wesselink method to the observations yields M_v=-3.86+/-0.2. Using spectroscopic observations spanning almost 7yr, we have discovered that ST Pup is a single-lined spectroscopic binary. The orbital period, 410.4+/-2.9d, is considerably longer than that of the other three known binary Type II Cepheids, which average about 100d. It has a very low orbital eccentricity, implying that orbital circularization and mass transfer have already taken place in this system. We estimate that [Fe/H]=-1.47+/-0.13 from a local thermodynamic equilibrium (LTE) fine analysis of high-resolution spectra obtained near minimum light. The value of C/O is 0.3, demonstrating that ST Pup is not a carbon star even though it displays strong CH and CN bands near minimum light. Most of the elements show an abundance pattern that correlates with condensation temperature similar to that of diffuse interstellar clouds and peculiar high-latitude A-F supergiants, which have been interpreted as low-mass post-AGB stars that have undergone selective mass-loss via grain formation. However, the Ca/Ti abundance ratio in the atmosphere of ST Pup is too high to be consistent with this interpretation. The Ca anomaly may have been caused by overionization of Ca^+ by Lyalpha photons when the star was losing mass. An infrared excess is seen at the JHKL and IRAS bands, indicating the presence of dust spanning a large range in distance from ST Pup.