To be able to control spreading phenomena (like the spreading of diseases and information) in networks it is important to identify influential spreaders. What "important" means depends on what is spreading and what kind of countermeasures that are available. In this work, we let the susceptible-infected-removed (SIR) model represent the spreading dynamics and contrast three different definitions of importance: Influence maximization (the expected outbreak size given a set of seed nodes), the effect of vaccination (how much deleting nodes would reduce the expected outbreak size) and sentinel surveillance (how early an outbreak could be detected with sensors at a set of nodes). We calculate the exact expressions of these quantities, as functions of the SIR parameters, for all connected graphs of three to seven nodes. We obtain the smallest graphs where the optimal node sets are not overlapping. We find that: node separation is more important than centrality for more than one active node, that vaccination and influence maximization are the most different aspects of importance, and that the three aspects are more similar when the infection rate is low. Furthermore, we discuss similar approaches to study the extinction times in the susceptible-infected- susceptible model.