We provide a band structure with low-energy properties consistent with recent photoemission and quantum oscillations measurements on FeSe, assuming mean-field like s and/or d-wave orbital ordering at the structural transition. We show how the resulting model provides a consistent explanation of the temperature dependence of the measured Knight shift and the spin-relaxation rate. Furthermore, the superconducting gap structure obtained from spin fluctuation theory exhibits nodes on the electron pockets, consistent with the 'V'-shaped density of states obtained by tunneling spectroscopy on this material, and the temperature dependence of the London penetration depth. Our studies prove that the recent experimental observations of the electronic properties of FeSe are consistent with orbital order, but leave open the microscopic origin of the unusual band structure of this material. ; Comment: 12 pages, 15 figures, T.B hopping error corrected, d-wave orbital order added, real space hoppings included in tex file