Graphene on an insulating ferromagnetic substrate-ferromagnetic insulator or ferromagnetic metal with a tunnel barrier-is expected to exhibit large exchange and spin-orbit couplings due to proximity effects. We use a realistic transport model of charge-disorder scattering and solve the linearized Boltzmann equation numerically exactly for the anisotropic Fermi contours of modified Dirac electrons to find magnetotransport signatures of these proximity effects: proximity anisotropic magnetoresistance, inverse spin-galvanic effect, and the planar Hall resistivity. We establish the corresponding anisotropies due to the exchange and spin-orbit couplings, with respect to the magnetization orientation. We also present parameter maps guiding towards optimal regimes for observing transport magnetoanisotropies in proximity graphene.