Magnetocaloric effects are of great interest for magnetic refrigeration as well as thermomagnetic energy production. Materials based on MnCoGe have been shown to be promising candidates in this respect. In this study, structural, electronic, and magnetic properties of MnCoGe alloys with several compositions (stoichiometric and Mn-depleted) have been investigated using first-principles calculations based on density functional theory. Their stability in the orthorhombic and hexagonal structure has been determined for different spin configurations. In all materials, the ferromagnetic orthorhombic phase is most stable; however, variation of the composition can lead to a decrease of the energy difference between the equilibrium orthorhombic and hexagonal structure. The magnetic moment is primarily found on the Mn atoms leading to a decrease of the total magnetic moment with decreasing amount of Mn. Using the Boltzmann transport model and the electronic density of states, the spin Seebeck coefficient has been estimated. At room temperature, it is found to be highest in stoichiometric MnCoGe in the orthorhombic crystal structure.