How should I configure CiviMember so both individuals and organizations can hold memberships?
I think the missing piece of your puzzle is to enable CiviCRM's inherited membership functionality. 


Create a membership type that will be inherited from your organization members.
Set the relationship type to Employer of.
Your organizations' staff will now be considered members, which allows you to send them emails, and lets them renew their employer's membership online.


You can read more about this in the user and administrator guide.