Plan your system groups before you begin creating them. Groups can make administration easier, but once you start using the system, it is harder to change your group organization. In general, create as few user groups as possible. Groups should be made for people who need to share files on the system, such as people who work in the same department, or people who are working on the same project. Though users can be in more than one group at a time, as in this case, they can only have one primary group at a time.
Users can change their primary group with the newgrp command.
It is also recommended for simple systems that you do not set the admin characteristic when creating groups. There are several system-defined groups. The other system-defined groups are used to control certain subsystems. Consult the subsystem information to see if certain users should be defined as a member of those groups. These permissions are controlled through the chmod command.