Selection of only one child record among those with the same parent

I want to create a parent / child relationship, where the child records represent different options of the parent record. At any given time, only one option should be the selected as the primary or 'go forward' option. But, I need to be able to change which child record is the primary at any given time. I know I can create a checkbox and then simply check the record that is primary, but then I will have to manually ensure that no other record is checked at the same time. And, I will have to manually ensure that there is always one record that is checked. What I am hoping to accomplish is that when I check/select a record to be the primary, all other related child records (with same parent) will automatically uncheck/unselect to ensure that only one child record can ever be primary at one time. But I also have to make sure that there is always one selected child record for a given parent. Presumably, the first child record created under a parent can automatically be selected/checked as the primary, and then I have the option to change the primary to subsequent child records as they are created.