While advancements in the prediction of wind turbine loads within the Actuator Line Method – Large Eddy Simulation (ALM-LES) framework have been an active research topic in recent years, the modelling of the tower and nacelle within ALM-LES simulations has received comparatively less attention. There is significant evidence that the support structure influences wind turbine aerodynamics across various scales: it affects the unsteady loading of the rotor, the wake structure and breakdown \cite{}, as well as the momentum availability and turbulence at the farm scale \cite{}. In this work, different methods used to model the support structure of a wind turbine, i.e. the tower and nacelle, are compared in terms of their effects on the subsequent wake development. Four support structure modelling methods from the literature are employed: (1) using the actuator line and disc methods to model the tower and nacelle, respectively; (2) modelling the tower using the ALM, as in (1), with additional introduction of an unsteady component in lift and drag, based on a characteristic Strouhal frequency; (3) modelling the support structure using an immersed-boundary method; and (4) explicitly resolving the support structure geometry. The methods are applied for the modelling of the NTNU Blind Test 1 (BT1) \cite{Krogstad2013}. While method (4) improves the accuracy of the predictions in the central part of the near wake as well as the overall far wake flow statistics, care must be taken when applying parametric methods such as (1)-(3). As a small experimental rotor, BT1 employs a tower-to-rotor diameter ratio (DT/DR) larger than what is typically encountered in utility scale rotors. This enhances the interaction between the rotor and support structure wake, making the BT1 dataset a useful experimental resource for the study of support structure influence. However, our understanding of the impact of support structures on utility scale rotors remains limited. Conclusions from the analysis of BT1 are used to capture support structure influence for cases with smaller DT/DR ratios, that correspond to utility scale rotors. This work aims to provide a clearer understanding of trade-offs associated with the various modelling methods used for the incorporation of towers and nacelles in ALM-LES simulations. Processing of full 3D flow fields of wakes, and comparison with experiments allows for an improved understanding of the interaction between the rotor and support structure wake