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Gas turbines are expected to play a key role in the energy production scenario in the future, and the introduction of carbon-free fuels is fundamental for the development of a sustainable energy mix. The development of a reliable numerical model is thus fundamental in order to support the design changes required for the burners. This paper presents the results of a numerical investigation on a turbulent, diffusive, combustion test case, with the purpose of identifying the best compromise between accuracy and computational cost, in the perspective of the model application in real, more complex, geometries. Referring to a test case has two main advantages. First, a rather simple geometry can be considered, still retaining a few peculiar flow features, such as recirculation vortices and shear layers, which are typical of real applications. Second, the experimental setup is much more detailed than in the case of real turbines, allowing a thorough model validation to be performed. In this paper, the Standard 2-equations k-ε model and the Speziale-Sarkar-Gatski Reynolds Stress Model are considered. Moreover, both the FGM combustion model and the detailed chemistry model are used, coupled with two chemical reaction mechanisms, and their results are compared. Finally, a standard and an enhanced near-wall approach are employed to solve the transport equations close to the walls. The results show a good agreement in the temperature distribution at the axial positions corresponding to the experimental measurements. Overall, the standard wall function approach for describing the near-wall flow proved to be more effective at increasingly higher distances from the jet centre. Such differences are related to the formulations employed by the two near-wall approaches, which led to changes in the predicted flow field around the fuel jet. Finally, the adoption of a reaction mechanism describing in detail the species concentration is mandatory whenever the reliable prediction of the NOx formation is of primary importance. The conclusion reached in this paper can be helpful for the development of reliable and cost-effective CFD models of turbine combustors.