We use first-principles calculations to show that van der Waals (vdW) heterostructures consisting of few-layer Bi₂Se₃ and PtSe₂ exhibit electronic and spintronics properties that can be tuned by varying the constituent layers. Type-II band alignment with layer-tunable band gaps and type-III band alignment with spin-splittings have been found. Most notably, we reveal the coexistence of Rashba-type spin-splittings (with large α_R parameters) in both the conduction and valence band stemming from few-layer Bi₂Se₃ and PtSe₂, respectively, which has been confirmed by spin-texture plots. We discuss the role of inversion symmetry breaking, changes in orbital hybridization, and spin–orbit coupling in altering electronic dispersion near the Fermi level. Since low-temperature growth mechanisms are available for both materials, we believe that few-layer Bi₂Se₃/PtSe₂ vdW heterostructures are feasible to realize experimentally, offering great potential for electronic and spintronics applications.