For Eigen solver setup you assign also the starting (minimum) frequecny so usually you can start with 10 or 20 modes without a precise meshing (fast simulation with lower passes number). From this, you can estimate the resonating frequeucnies for all the modes and see roughly how many modes are lying in your interested band of frqeuencies and hence decide the reasonable number of modes which you will use for your final simulation.
it depends on the structures you re analyzing, for example, if it is a waveguide, you can have a rough mathematical approximation for the cutoff. If it is another structure and support and you are searching for specific mode (for example TE30) and do not have any theatrical calculation you can start with anyone freq and check the mode then increase or decrease the freq depending on the mode you are getting