Mg batteries with oxide cathodes have the potential to significantly surpass existing Li-ion technologies in terms of sustainability, abundance, and energy density. However, Mg intercalation at the cathode is often severely hampered by the sluggish kinetics of Mg$^{2+}$ migration within oxides. Here we report a combined theoretical and experimental study addressing routes to identify cathode materials with an improved Mg-ion mobility. Using periodic density functional theory calculations, Mg$^{2+}$ migration in oxide spinels has been studied, revealing key features that influence the activation energy for M$^{g2}$+ migration. Furthermore, the electronic and geometrical properties of the oxide spinels as well as their stability have been analyzed for a series of different transition metals in the spinels. We find that electronegative transition metals enable a high Mg-ion mobility in the oxide spinel frameworks and thus a favorable cathode functionality. Based on the theoretical findings, some promising candidates have been identified, prepared and structurally characterized. Our combined theoretical and experimental findings open up an avenue toward the utilization of functional cathode materials with improved Mg$^{2+}$ transport properties for Mg-metal batteries.