In this paper we investigate the emission and detection characteristics of prompt gamma (PG) rays for in vivo range verification during hadron therapy, using Geant4 simulations. Proton, 4 He and 12 C beams of varying energy are incident on water phantoms. The PG production yield, energy spectral characteristics and spatial correlation with the Bragg Peak (BP) have been quantified. Further, the angular distributions for PG detection with respect to a point-of-reference on the phantom surface have been explored. The temporal properties of PG emission and time-of-flight (TOF) of PG detection have also been investigated in correlation with the changing particle beam range. Our results show that the primary PG rays from nuclear interactions of the primary beam exhibit the closest correlation to the beam range but its signal is significantly masked by the concurrent secondary PG rays, particularly for heavier ions such as carbon ion beams. The PG TOF spectroscopy encodes the essential information of the beam range but requires high time resolution measurements to retrieve it. A hybrid PG detection system to utilize the energy, timing and spatial characteristics of PG rays is desirable for BP tracking in real-time.