This paper proposes a new multi-objective stochastic market settlement model for a coupled energy and reactive power ancillary service, named as MOSMS-CERP model, for a prospective grid integration of wind energy. It is a comprehensive two-stage scenario-based stochastic optimization model to incorporate the system uncertainties associated with wind power generations along with load demands. In this multi-objective framework, two competing objective functions as the expected total payment functions for energy and reactive power ancillary services are simultaneously minimized while satisfying all the system operating constraints including technical as well as market driven constraints. An efficient hybrid payment strategy is designed for energy market as well as reactive power ancillary service market for creating a competitive and fair market auction. A pay-as-bid payment mechanism is adopted for all thermal generating units whereas a pay-at-MCP (Market Clearing Price) is adopted for all hydro-powered generating units and wind farms for the energy market settlement. However, the ancillary service market of reactive power is settled using uniform price payment mechanism. It is a unique market settlement model, which combines three significant complexities such as stochastic nature, multi-objective constrained optimization, and meta-heuristics. The proposed MOSMS-CERP model is examined by applying five well-known, recent, and advanced meta-heuristic methods such as Non-dominated Sorting Genetic Algorithms (NSGA-II & I-NSGA-III), Multi-Objective Keshtel Algorithm (MOKA), Hybrid Fuzzy Multi-Objective Evolutionary Algorithm (HFMOEA), and Multi-Objective Particle Swarm Optimization (MOPSO) for producing the sets of Pareto-optimal solutions. A fair statistical comparison is carryout for these five meta-heuristic methods based on No Free Launch Theorem. All simulations are conducted on a standard IEEE 24-bus RTS with a doubly fed induction generator (DFIG) based wind farm on a DIgSILENT Power Factory software platform. The obtained simulation results ensure the robustness and effectiveness of the proposed MOSMS-CERP model.