As a conducive and prevalent technique for producing green hydrogen, hybrid wind-based electrolyser system requires both effective planning and operation to realize its techno-economic value. Majority of the existing studies are focused on either of these two, but none of them sufficiently emphasize on their interrelationship. In this paper, we propose a two-stage multi-objective optimization framework to reveal optimal investment plans considering various operational strategies, such as economic revenue maximization and green hydrogen production maximization. The results reveal that: 1) A trade-off exists between system investment and the capacity to accomplish optimal operational performance. For example, the system demands flexibility to boost operational profits, but this results in high investment costs. 2) Differentiated operation objectives generate different component capacities during the planning phase. 3) Regarding a wind-hydrogen system with gas storage, the Pareto optimal design manifesting the trade-off between system investment and prime operational performance can be actualized along the margins of a feasible solution.