We perform first-principles calculations to determine the electronic, magnetic, and transport properties of rare-earth dichalcogenides, taking a monolayer of $H$-phase ${\mathrm{EuS}}_{2}$ as a representative. We predict that the $H$ phase of the ${\mathrm{EuS}}_{2}$ monolayer exhibits a half-metallic behavior upon doping with a very high magnetic moment. We find that the electronic structure of ${\mathrm{EuS}}_{2}$ is very sensitive to the value of Coulomb repulsion $U$, which effectively controls the degree of hybridization between Eu $f$ and S $p$ states. We further predict that the nontrivial electronic structure of ${\mathrm{EuS}}_{2}$ directly results in a pronounced anomalous Hall effect with nontrivial band topology. Moreover, while we find that the spin Hall effect closely follows the anomalous Hall effect in the system, the orbital complexity of the system results in a very large orbital Hall effect, whose properties depend very sensitively on the strength of correlations. Our findings thus promote rare-earth-based dichalcogenides as a promising platform for topological spintronics and orbitronics.