The unit of molar mass depends on what you are trying to calculate. For most high school level calculations grams/mole is the better unit to use. In any calculation you should write out the units of all the parts of the calculation and then see if all the units cancel out correctly leaving you with the unit you want your answer in. For example when working out number of moles, you would use moles = mass divided by molar mass. The units would be moles =grams divided by grams/mole which gives the correct unit for the answer.