We report the synthesis and structural and magnetic characterization of model square or rectangular antiferromagnets [BDTA]2[MCl4] [BDTA = benzo-1,3,2-dithiazolyl; M = Cu (1), Co (2), and Mn (3)]. All of these compounds display a molecular structure of sandwich layers of [MCl4]2- between two sheets of [BDTA]+ molecules. Consideration of likely superexchange pathways suggests that 1 presents a model square lattice of S = 1/2 moments, while 2 and 3 present model rectangular lattices with S = 3/2 and 5/2, respectively. Magnetic susceptibility measurements indicate that all of these materials have modest antiferromagnetic exchange fields, with near-neighbor exchange J/k(B) running from 0.018(1) through 0.35(3) to 2.10(2) K as M runs from Mn to Co to Cu. No signature of any three-dimensional magnetic ordering could be observed down to 1.8 K. 1 is of particular interest because it belongs to a similar class of magnets as the high-Tc superconducting cuprates but has a much smaller exchange field; it has been proposed that the application of a magnetic field to this type of magnet can induce novel quantum states in this class of magnet, but the observation of such states is only experimentally feasible for small exchange. More detailed characterization of 1 by heat capacity measurements showed a broad cusp centered at 1.3 K in the absence of an applied magnetic field but failed to observe any sign of long-range order down to 0.33 K; this suggests that interplane magnetic exchange is weak.