How would you choose between two characteristics to be used for developing a hierarchy in classification?

Before developing a hierarchy in classification, we need to decide which characteristics should be used as the basis for making the broadest divisions. Then we should pick up next set of characteristics for making subgroups. This process must continue and each time new characteristics should be used. The
characteristics that decide the broadest divisions among living organisms should be independent of any other characteristics. For example, nature of cell and form of the body is considered to classify organisms into broad divisions (e.g., Prokaryotes and Eukaryotes). The characteristics of the next level should be
dependent on the previous one that will decide the subsequent divisions of the groups.