New charge-transfer salts based on an unsymmetrical donor DMET [dimethyl(ethylenedithio)diselenadithiafulvalene] and metal halide anions (DMET)4MIICl4(TCE)2 (M = Mn, Co, Cu, Zn; TCE = 1,1,2-trichloroethane) have been synthesized and characterized by transport and magnetic measurements. The crystal structures of the DMET salts are isostructural, consisting of a quasi-one-dimensional stack of DMET and insulating layers containing metal halide anions and TCE. Semimetallic band structures are calculated by the tight-binding approximation. Metal-insulator transitions are observed at TMI = 25, 15, 5-20, and 13 K for M = Mn, Co, Cu, and Zn, respectively. The M = Cu salt exhibits anisotropic conduction at ambient pressure, being semiconducting in the intralayer current direction but metallic for the interplane current direction, down to T(MI). The metal-insulator transitions are suppressed under pressure. In the M = Co and Zn salts, large magnetoresistances with hysteresis are observed at low temperatures, on which Shubnikov-de Haas oscillations are superposed above 30 T. In the M = Cu salt, no hysteresis is observed but clear Shubnikov-de Haas oscillations are observed. The magnetoresistance is small and monotonic in the M = Mn salt. Paramagnetic susceptibilities of the spins of the magnetic ions are observed for the M = Mn, Co, and Cu salts with small negative Weiss temperatures of approximately 1 K. In the nonmagnetic M = Zn salt, Pauli-like pi-electron susceptibility that vanishes at TMI is observed. The ground state of the pi-electron system is understood as being a spin density wave state caused by imperfect nesting of the Fermi surfaces. In this pi-electron system, the magnetic ions of the M = Mn, Co, and Cu salts interact differently, exhibiting a variety of transport behaviors.