Floating Offshore Wind Turbines (FOWT) can harness the abundant wind resource in deep-water offshore conditions. However, they face challenges in harsh, unsheltered marine environments. The mean hydro- and aerodynamic loads coupled with fluctuating stochastic wind and wave loads contribute to varied failure mechanisms. Therefore, the serviceability, ultimate, and fatigue limit states are vital in ensuring the safety and reliability of FOWT. This paper investigates how specific loads and states drive the design of a spar-type support structure, utilising a computationally efficient frequency-domain model. This approach combines quasi-static aerodynamic and mooring models with a potential-theory-based radiation-diffraction solver. The serviceability criteria concern the platform and tower top displacements and accelerations. The ultimate and fatigue limit states are assessed for the tower base, the waterline section, and the mooring lines, including the effects of yielding under the bending moment and compressive axial load, column buckling, and tension-tension effects in the mooring lines. The full factorial design of experiments is employed to investigate the non-trivial relationships between the limit states and the various features of the support structure. The results demonstrate that the design of the spar platform above the waterline is mainly driven by fatigue, which results from significant dynamic tilt and increased stress concentration at the platform-tower intersection. On the other hand, the catenary mooring lines' design is mainly driven by the requirements of maximum offset (serviceability limit state) and fatigue.