The final possibility is to calculate the sum of squares conditional on the interaction. This is uncommon, as we typically aren't interested in the main effects given that a significant interaction exists. If the interaction is not significative, then Type II has more power:

If the underlying design is balanced (the same amount of observations for each factor combination), the three of them will be equivalent. If they are not, they will differ. In general, Type II is preferred since we want to test an effect after controlling the other one, but we can't test the interaction using it. So, we generally prefer Type I initially to test the interaction, and if it is found to be nonsignificative, we continue with Type II. On the other hand, if it is found to be significative, we can proceed with Type III, but whether it makes sense to make inferences on a main effect after an interaction is detected is questionable.

The anova and aov functions in R will work with the Type I sum of squares. To get Type II or Type III, we can use the anova function in the car package.