Four copper(II) complexes, C1–4, derived from 1-(isoquinolin-3-yl)heteroalkyl-2-one ligands L1–4 were synthesized and characterized using an elemental analysis, IR spectroscopic data as well as single crystal X-ray diffraction data for complex C1. The stability of complexes C1–4 under conditions mimicking the physiological environment was estimated using UV-Vis spectrophotometry. The antiproliferative activity of both ligands L1–4 and copper(II) compounds C1–4 were evaluated using an MTT assay on four human cancer cell lines, A375 (melanoma), HepG2 (hepatoma), LS-180 (colon cancer) and T98G (glioblastoma), and a non-cancerous cell line, CCD-1059Sk (human normal skin fibroblasts). Complexes C1–4 showed greater potency against HepG2, LS180 and T98G cancer cell lines than etoposide (IC50 = 5.04–14.89 μg/mL vs. IC50 = 43.21–>100 μg/mL), while free ligands L1–4 remained inactive in all cell lines. The prominent copper(II) compound C2 appeared to be more selective towards cancer cells compared with normal cells than compounds C1, C3 and C4. The treatment of HepG2 and T98G cells with complex C2 resulted in sub-G1 and G2/M cell cycle arrest, respectively, which was accompanied by DNA degradation. Moreover, the non-cytotoxic doses of C2 synergistically enhanced the cytotoxic effects of chemotherapeutic drugs, including etoposide, 5-fluorouracil and temozolomide, in HepG2 and T98G cells. The antimicrobial activities of ligands L2–4 and their copper(II) complexes C2–4 were evaluated using different types of Gram-positive bacteria, Gram-negative bacteria and yeast species. No correlation was found between the results of the antiproliferative and antimicrobial experiments. The antioxidant activities of all compounds were determined using the DPPH and ABTS radical scavenging methods. Antiradical tests revealed that among the investigated compounds, copper(II) complex C4 possessed the strongest antioxidant properties. Finally, the ADME technique was used to determine the physicochemical and drug-likeness properties of the obtained complexes.