In Virtual Reality, a number of studies have been conducted to assess the influence of avatar appearance, avatar control and user point of view on the Sense of Embodiment (SoE) towards a virtual avatar. However, such studies tend to explore each factor in isolation. This paper aims to better understand the interrelations among these three factors by conducting a subjective matching experiment. In the presented experiment (n=40), participants had to match a given "optimal" SoE avatar configuration (realistic avatar, full-body motion capture, first-person point of view), starting by a "minimal" SoE configuration (minimal avatar, no control, third-person point of view), by iteratively increasing the level of each factor. The choices of the participants provide insights about their preferences and perception over the three factors considered. Moreover, the subjective matching procedure was conducted in the context of four different interaction tasks with the goal of covering a wide range of actions an avatar can do in a VE. The paper also describes a baseline experiment (n=20) which was used to define the number and order of the different levels for each factor, prior to the subjective matching experiment (e.g. different degrees of realism ranging from abstract to personalised avatars for the visual appearance). The results of the subjective matching experiment show that point of view and control levels were consistently increased by users before appearance levels when it comes to enhancing the SoE. Second, several configurations were identified with equivalent SoE as the one felt in the optimal configuration, but vary between the tasks. Taken together, our results provide valuable insights about which factors to prioritize in order to enhance the SoE towards an avatar in different tasks, and about configurations which lead to fulfilling SoE in VE.