Methanol is an important chemical compound which is used both as a fuel and as a platform molecule in chemical production. Synthesizing methanol, as well as dimethyl ether, directly from carbon dioxide and hydrogen produced using renewable electricity would be a major step forward in enabling an environmentally sustainable economy. We utilize density functional theory combined with microkinetic modeling to understand the methanol synthesis reaction mechanism on a model CoGa catalyst. A series of catalysts with varying Ga content are synthesized and experimentally tested for catalytic performance. The performance of these catalysts is sensitive to the Co:Ga ratio, whereby increased Ga content results in increased methanol and dimethyl ether selectivity and increased Co content results in increased selectivity towards methane. We find that the most active catalysts have up to 95% CO-free selectivity towards methanol and dimethyl ether during CO2 hydrogenation and are comparable in performance to a commercial CuZn catalyst. Using in situ DRIFTS we experimentally verify the presence of a surface formate intermediate during CO2 hydrogenation in support of our theoretical calculations.