Why don't Organisations have Contacts?
Yes, you have to set up an organization and then an individual. Next step is then to link them with a relationship.  You can either use the relationship tab and add one, or fill in the name of the organization in the "employer" box when you add an individual. The latter will automatically create a relationship of the type "Employee/Employer".

As CiviCRM is targeted at non-profits it does not automatically work with leads :-) In quite a lot of cases the term "lead" would mean absolutely nothing.