The reactions of picolinyl and 4-chloropicolinyl chlorides with methyl esters of S-methyl-l-cysteine, l- and d-methionine, and l-histidine afforded a series of functionalized carboxamides, which readily formed pincer-type complexes upon interaction with PdCl2(NCPh)2 in solution under mild conditions. The direct cyclopalladation of the ligands derived was also accomplished in the solid phase, in particular, mechanochemically, although it was complicated by the partial deactivation of the starting amides. The resulting complexes with 5,5- and 5,6-membered fused metallocycles were fully characterized by IR and NMR spectroscopy, including variable-temperature and 2D-NMR studies. In the case of some cysteine- and methionine-based derivatives, the realization of κ3-N,N,S-coordination was supported by X-ray diffraction. The cytotoxic effects of these complexes were examined on HCT116, MCF7, and PC3 human cancer cell lines as well as HEK293 as a representative of normal cells. The comparative studies allowed us to determine that the presence of the sulfide ancillary donor group is crucial for cytotoxic activity of this type of Pd(II) complexes. The main structure-activity relationships and the most promising palladocycles were outlined. The additional studies by gel electrophoresis revealed that 4-chloropicolinyl derivatives, despite the nature of an amino acid, can bind with DNA and inhibit topoisomerase I activity.