By taking subsidies out of the picture, wind farm operators (WFO) face new challenges to participate in electricity markets. While conventional producers benefit from dispatchable generation, wind farms with stochastic nature have a challenging job to compete with these players in the market and need to come up with alternative solutions. To this end, energy storage devices have a great potential in managing the volatile generation and thereby increasing the profit of WFOs. On the other hand, the gas market opens new opportunities to improve the flexibilities of WFOs in addressing the incurred penalties due to deviation between prediction and generation. For the sake of practicality, this paper proposes a joint operation-planning model. The WFO bids in both the day-ahead electricity market and gas market while also invests in alternative facilities, including electrical energy storage, gas storage, power-to-gas, and gas-to-power. The proposed framework is formulated as a mixed-integer nonlinear programming (MINLP) model. To guarantee to find the global solution, the original MINLP model is recast into a mixed-integer linear programming (MILP) model. Several case studies are defined to capture the potential of the proposed framework on the profit of the WFO, scrutinizing the performance of different facilities and interactions with the aforementioned markets. The modeling provides a tool for the WFOs for considering different alternative approaches to deal with uncertainty of generation. This includes storing the surplus generation of wind farm in the form of electricity through electrical energy storage or by converting this surplus into gas via power-to-gas technology and either store it in a gas storage or sell it in the gas market. Moreover, under the lack of generation condition, the electrical energy storage can provide electricity, or the gas from gas market and gas storage can turn to electricity through gas-to-power facility to assist WFOs. Results show the effectiveness of the proposed framework in enhancing the profitability of wind farms via different alternatives while highlighting the role of the gas market as a promising solution.