A set of copper(I) complexes with the general formula [CuBr(PPh3)(N^N)] (N^N = 2,2’-bipyridine (1), 1,10-phenanthroline (2), 4,4’-dimethyl-2,2’-bipyridine (3), 4,4’-dimethoxy-2,2’-bipyridine (4), 3-(2-pyridyl)-4,5-diphenyl-1,2,4-triaine (5), 4,7-diphenyl-1,10-phenanthroline (6), 5-nitro-1,10-phenanthroline (7), dipyrido[3,2-a:2',3'-c]phenazine(8)) have been synthesized and characterized by elemental analysis, 31P-NMR spectroscopy and mass spectrometry. The structure of complexes 5 and 7 were confirmed by X-ray crystallography. Complex 5 is the second example to be reported with an unusual 4N-triazine-ligated coordination mode of the 3-(2-pyridyl)-4,5-diphenyl-1,2,4-triazine. Calculated energies of the two possible bidentate modes of the ligand (2N- and 4N-triazine) at the copper center showed no significant difference, rationalizing that with the absence of the steric hindrance effect around the metal center. Preliminary biological studies were conducted, highlighting the effect of the diimine ligands. Complexes 5 and 8 exhibited good cytotoxicity against prostate (PC-3), leukemia (MOLT-4) and breast (MCF-7) cancer cell lines, consistent with the presence of nitrogen heteroatoms and extended delocalized systems correlating with strong cytotoxic performance. Binding affinity studies against ct-DNA and docking studies with B-DNA and MDM2 protein highlighted the strong p interactions of 5 and 8, with the planarity of the diimine ligand of the latter contributing to its better binding and cytotoxicity. The current results afford structural requirements for the design of new copper(I) complexes with enhanced biological/physiochemical properties.