In this paper, we perform a systematic and rigorous study to evaluate the Ohmic nature of the top-contact formed by the monolayer ReS2 (mReS2) and metals (gold, silver, platinum, nickel, titanium, and scandium) by means of first-principles density functional theory calculations. We investigate the potential barrier, charge transfer and atomic orbital overlap at the mReS2-metal interface in consideration of van der Waals forces to understand how efficiently carriers could be injected from the metal contact to the mReS2 channel. ReS2 is physisorbed on Au and Ag, which leads to little perturbation of its electronic structures and forms a larger Schottky contact and a higher tunnel barrier at the interface. ReS2 is chemisorbed on Ti and Sc, where the bonding strongly perturbs the electronic structures and is found to be purely Ohmic. The bonding of ReS2 on Pt and Ni lies between these two extreme cases, demonstrating an intermediate behavior. These findings not only provide an insight into the mReS2-metal interfaces but may also prove to be instrumental in the future design of ReS2-based devices with good performance.