Despite recent experimental evidence for an anisotropic component in the ultra-high-energy cosmic ray (UHECR) sky for energies above a few EeV, the nature and distribution of UHECR sources are still not well understood. Identification of cosmic particle accelerators in the sky is complicated by UHECR interactions with background photon fields and by the deflection in extragalactic and galactic magnetic fields (EGMF and GMF). Moreover, the spatial structure of the EGMF is not yet well understood, which makes the back-tracking of UHECRs a non-trivial task. In this work we study the propagation of UHECRs for a range of UHECR source distributions and EGMF models. We simulate extragalactic UHECR propagation and interactions by using the Monte Carlo code CRPropa3. UHECR deflection in the GMF is taken into account by mapping arrival directions at the edge of the Milky Way to those at Earth for particular GMF models. We then predict the anisotropy observables of the propagated UHECRs at Earth for various combinations of source catalogues, injected energy and mass distributions, and EGMF models. Based on this, the impact of the different model ingredients on the observables is discussed. Comparison with UHECR data will eventually allow us to put further constraints on scenarios for the source and EGMF distributions.