We have obtained near-infrared spectra covering the Ca II triplet lines for a large number of stars associated with 16 Small Magellanic Cloud (SMC) clusters using the VLT + FORS2. These data compose the largest available sample of SMC clusters with spectroscopically derived abundances and velocities. Our clusters span a wide range of ages and provide good areal coverage of the galaxy. Cluster members are selected using a combination of their positions relative to the cluster center as well as their location in the color-magnitude diagram, abundances, and radial velocities (RVs). We determine mean cluster velocities to typically 2.7 km s −1 and metallicities to 0.05 dex (random errors), from an average of 6.4 members per cluster. By combining our clusters with previously published results, we compile a sample of 25 clusters on a homogeneous metallicity scale and with relatively small metallicity errors, and thereby investigate the metallicity distribution, metallicity gradient, and age-metallicity relation (AMR) of the SMC cluster system. For all 25 clusters in our expanded sample, the mean metallicity [Fe/H] = −0.96 with σ = 0.19. The metallicity distribution may possibly be bimodal, with peaks at ∼−0.9 dex and −1.15 dex. Similar to the Large Magellanic Cloud (LMC), the SMC cluster system gives no indication of a radial metallicity gradient. However, intermediate age SMC clusters are both significantly more metal-poor and have a larger metallicity spread than their LMC counterparts. Our AMR shows evidence for three phases: a very early (> 11 Gyr) phase in which the metallicity reached ∼−1.2 dex, a long intermediate phase from ∼10 to 3 Gyr in which the metallicity only slightly increased, and a final phase from 3 to 1 Gyr ago in which the rate of enrichment was substantially faster. We find good overall agreement with the model of Pagel & Tautvaišiene, which assumes a burst of star formation at 4 Gyr. Finally, we find that the mean RV of the cluster system is 148 km s −1 , with a velocity dispersion of 23.6 km s −1 and no obvious signs of rotation amongst the clusters. Our result is similar to what has been found from a wide variety of kinematic tracers in the SMC, and shows that the SMC is best represented as a pressure supported system.