We report the cooling-induced crystallization of layered two-dimensional lead halide perovskites with controllable inorganic quantum-well thickness (n = 1, 2, 3, 4), organic spacer chain length (butyl-, pentyl-, hexylammonium), A-site cation (methylammonium, formamidinium), and halide anion (iodide, bromide). We report crystal structures for the iodide family as a function of these compositional parameters, and across their temperature dependent phase transitions. In general, lower symmetry crystal structures, increasing extents of organic-spacer interdigitation, and increasing organic-spacer corrugation tilts are observed at low temperature. In addition, greater structural distortions are seen in lead halide octahedra closest to the organic spacer layer, and larger-n structures exhibit periodic variation in Pb-I bond lengths. We also provide detailed guidance regarding the combination of synthetic parameters needed to achieve phase-pure crystals of each composition, and discuss difficulties encountered when trying to synthesize particular members of the 2D perovskite family containing formamidinium or cesium as the A-site cation. These results provide a foundation for understanding structural trends in 2D lead halide perovskites and the effect these trends have on their thermal, electrical, and optical properties.