A theory for Frenkel exciton dynamics in molecular aggregates which incorporates coupling to vibrational motions (intramolecular, intermolecular and solvent) with multiple spectral densities of arbitrary nature and interpolates between the coherent and the incoherent limits is developed. A rigorous procedure for identifying the relevant collective nuclear coordinates necessary to represent a given set of spectral densities is obtained. Additional coordinates are required as the temperature is lowered. Exciton dynamics is calculated by following the evolution of wavepackets representing the electronic density matrix in the collective coordinates phase space. The signatures of excitonic and nuclear motions in ultrafast fluorescence spectroscopy are explored using a hierarchy of reduction schemes with varying numbers of collective coordinates.