With the increase of wind power installed capacity and the development of energy storage technologies, it is gradually accepted that integrating wind farms with energy storage devices to participate in spot electricity market (EM) is a promising way for improving wind power uncertainty accommodation and bringing considerable profit. Hence, research on reasonable offering and operating strategies for integrated wind farm-energy storage system (WF-ESS) under spot EM circumstances has important theoretical and practical significance. In this paper, a newly progressive stochastic-robust hybrid optimization model series is proposed for yielding such strategies. In the day-ahead stage, day-ahead and balancing prices uncertainties are formulated by applying joint stochastic scenarios, and real-time available wind power uncertainties are modeled by using the seasonal auto-regression (AR) based dynamic uncertainty set. Then, the first model of this model series is established and utilized for cooptimizing both the day-ahead offering and nominal real-time operating strategies. In the balancing stages, wind power uncertainty set and balancing prices stochastic scenarios are dynamically updated with the newly realized data. Then, each model from the remaining of this model series is established and utilized period by period for obtaining the optimal balancing/real-time offering/operating strategies adjusted from the nominal ones. Robust optimization (RO) in this progressive framework makes the operation of WF-ESS dynamically accommodate wind power uncertainties while maintaining relatively low computational complexity. Stochastic optimization (SO) in this progressive framework makes the WF-ESS avoid pursuing profit maximization strictly under the worst-case scenarios of prices uncertainties. Moreover, by adding a risk-aversion term in form of conditional value at risk (CVaR) into the objective functions of this model series, the optimization models additionally provide flexibility in reaching a trade-off between profit maximization and risk management. Simulation and profit comparisons with other existing methods validate the scientificity, feasibility, and effectiveness of applying our proposed model series.