Reed musical instruments are known to produce a wealth of sound regimes. In physical models, this complexity manifests itself by the coexistence of equilibrium, periodic and quasiperiodic regimes. From a musical perspective, controlling which regime is observed in practice when different stable regimes coexist for the same parameters can be particularly challenging. We consider a physical model of reed instrument, written as a low-order nonlinear dynamical system. A bifurcation analysis is performed to identify the multistable regions of the parameter space, where several stable regimes coexist. In these regions, the basins of attraction are investigated by means of support vector machine. The basin of a given regime corresponds to the set of initial conditions for which this regime is observed after any transient dynamics has died out, and relates to the fact that this regime is easily played in practice or not. We investigate how basins structure evolves when the mouth pressure dynamics (corresponding to attack transients) is taken into account, and highlight significant differences between the classical static basins (determined for constant values of the mouth pressure) and what we introduce as dynamical basins. In particular, some regimes are much easier to observe than predicted by the static case.