We investigate the evolution of magnetic excitations in Sr3Ru2O7 in the paramagnetic metallic phase using a three-band tight-binding model. The effect of Mn or Ti dopant ions on the Sr3Ru2O7 band structure has been included by taking into account the dopant-induced suppression of the oxygen octahedral rotation in the tight-binding band structure. We find that the low-energy spin fluctuations are dominated by three wave vectors around q - =((0,0),(π/2,π/2)) and (π,0), which compete with each other. As the octahedral rotation is suppressed with increasing doping, the three wave vectors evolve differently. In particular, the undoped compound has dominant wave vectors at q- =((0,0),(π/2,π/2)), but doping Sr3Ru2O7 leads to a significant enhancement in the spin susceptibility at the q - =(π,0) wave vector, bringing the system closer to a magnetic instability. All the features calculated from our model are in agreement with neutron scattering experiments. We have also studied the effect of a c-axis Zeeman field on the low-energy spin fluctuations. We find that an increasing magnetic field suppresses the antiferromagnetic (AFM) fluctuations and leads to stronger competition between the AFM and ferromagnetic spin fluctuations. The magnetic field dependence observed in our calculations therefore supports the scenario that the observed nematic phase in the metamagnetic region in Sr3Ru2O7 is intimately related to the presence of a competing ferromagnetic instability. © 2016 American Physical Society.