A series of four water-soluble salicylaldehyde thiosemicarbazones with a positively charged trimethylammonium moiety ([H2LR]Cl, R = H, Me, Et, Ph) and four copper(II) complexes [Cu(HLR)Cl]Cl (1–4) were synthesised with the aim to study (i) their antiproliferative activity in cancer cells and, (ii) for the first time for thiosemicarbazones, the interaction with membrane transport proteins, specifically organic cation transporters OCT1–3. The compounds were comprehensively characterised by analytical, spectroscopic and X-ray diffraction methods. The highest cytotoxic effect was observed in the neuroblastoma cell line SH-5YSY after 24 h exposure and follows the rank order: 3 > 2 > 4 > cisplatin > 1 >> [H2LR]Cl. The copper(II) complexes showed marked interaction with OCT1–3, comparable to that of well-known OCT inhibitors (decynium 22, prazosin and corticosterone) in the cell-based radiotracer uptake assays. The work paves the way for the development of more potent and selective anticancer drugs and/or OCT inhibitors.