In anticipation of the upcoming 2018 InSight (Interior exploration using Seismic Investigations, Geodesy and Heat Transport) Discovery mission to Mars, we calibrate magnitude scales for marsquakes that incorporate state-of-the-art knowledge on Mars interior structure and the expected ambient and instrumental noise. We regress magnitude determinations of 2600 randomly distributed marsquakes, simulated with a spectral element method for 13 published 1D structural models of Mars' interior. The continuous seismic data from InSight will be returned at 2 samples per second. To account for this limited bandwidth as well as for the expected noise conditions on Mars, we define and calibrate six magnitude scales: (1) local Mars magnitude M-L(Ma) at a period of 3 s for marsquakes at distances of up to 10 degrees; (2) P-wave magnitude m(b)(Ma); (3) S-wave magnitude m(bS)(Ma) each defined at a period of 3 s and calibrated for distances from 5 degrees to 100 degrees; (4) surface-wave magnitude M-s(Ma) defined at a period of 20 s, as well as (5) moment magnitudes M-FB(Ma); and (6) M-F(Ma) computed from the low-frequency (10-100 s) plateau of the displacement spectrum for either body waves or body and surface waves, respectively; we calibrate scales (4)-(6) for distances from 5 degrees to 180 degrees. We regress stable calibrations of the six scales with respect to the seismic moment magnitude at M-w 5.5 by correcting filtered phase amplitudes for attenuation with distance and source depth. Expected errors in epicentral distance and in source depth (25% and 20 km, respectively) translate into magnitude errors of 0.1-0.3 units. We validate our magnitude relations with an independent test dataset of 2600 synthetic marsquakes (1.0 <= M-w <= 7.0), for which seismograms are superimposed on the realistic noise predicted by the InSight noise model. Marsquakes with M-w < 3.0 and epicentral distances of Delta > 15 degrees are expected to be hidden in the Mars background noise and will likely not be detectable.