A series of zinc(II) ([Zn(H2O)(L)Cl] (1)), copper (II) ([Cu(L)Cl] (2), [Cu(L)Br] (3), [Cu2(L)2(CH3COO)2]·4H2O (4)), nickel(II) ([Ni(HL)2]Cl2·H2O (5)), and cobalt(III) ([Co(L)2]Cl (6)) complexes were obtained with 2-formylpyridine N4-allylthiosemicarbazone (HL). In addition another two thiosemicarbazones (3-formylpyridine N4-allylthiosemicarbazone (HLa) and 4-formylpyridine N4-allylthiosemicarbazone (HLb)) have been obtained. The synthesized thiosemicarbazones have been studied using 1H and 13C NMR spectroscopy, IR spectroscopy, and X-ray diffraction analysis. The composition and structure of complexes were studied using elemental analysis, IR and UV-Vis spectroscopies, molar conductivity, and magnetic susceptibility measurements. Single crystal X-ray diffraction analysis elucidated the structure of thiosemicarbazones HL, HLa, and HLb, as well as complexes 4 and 5. The antiproliferative properties of these compounds toward a series of cancer cell lines (HL-60, HeLa, BxPC-3, RD) and a normal cell line (MDCK) have been investigated. The nickel complex shows high selectivity (SI > 1000) toward HL-60 cell line and is the least toxic. The zinc complex shows the highest selectivity toward RD cell line (SI = 640). The copper complexes (2–4) are the most active molecular inhibitors of proliferation of cancer cells, but exhibit not such a high selectivity and are significantly more toxic. Zinc and copper complexes manifest high antibacterial activity. It was found that calculated at B3LYP level of theory different reactivity descriptors of studied compounds strongly correlate with their biological activity.