The electrodeposition of lithium metal is a key process in next-generation, high energy density storage devices. However, the high reactivity of the lithium metal causes short cycling lifetimes and dendrite growth that can pose a serious safety issue. Recently, a number of approaches have been pursued to stabilize the lithium metal-electrolyte interface, including soft polymeric coatings that have shown the ability to enable high-rate and high-capacity lithium metal cycling, but a clear understanding of how to design and modify these coatings has not yet been established. In this work, we studied the effects of several polymers with systematically varied chemical and mechanical properties as coatings on the lithium metal anode. By examining the early stages of lithium metal deposition, we determine that the morphology of the lithium particles is strongly influenced by the chemistry of the polymer coating. We have identified polymer dielectric constant and surface energy as two key descriptors of the lithium deposit size. Low surface energy polymers were found to promote larger deposits with smaller surface areas. This may be explained by a reduced interaction between the coating and the lithium surface and thus an increase in the interfacial energy. On the other hand, high dielectric constant polymers were found to increase the exchange current and gave larger lithium deposits due to the decreased overpotentials at a fixed current density. We also observed that the thickness of the polymer coating should be optimized for each individual polymer. Furthermore, polymer reactivity was found to strongly influence the Coulombic efficiency. Overall, this work offers new fundamental insights into lithium electrodeposition processes and provides direction for the design of new polymer coatings to better stabilize the lithium metal anode.