The dynamics of a self-organised model of shoaling fish are explored within a Lagrangian (or individual based) framework in order to identify the key behavioural factors that shape its dynamic landscape. By exploring systematically all possible initial states we identify the transitions to and between the different possible stationary states (schooling vs. swarming or milling). The route to these stationary states is explained from an individual perspective. On the behavioural level we discuss in particular the decisive impact of two traits, the perception angle and the manoeuvrability of the fish. A key result of this study is that the fish density in certain stationary states reaches values where each fish perceives each other; local interactions actually become global interactions. We further discuss the specific value of such Lagrangian studies in comparison to analytical approaches, in particular the freedom to include any important biological trait and the importance of an exhaustive numerical investigation.