There is no form available on the User's tab that allows me to add users.
All I have is a smaller form which is to invite users to the new site, but when they click on the emailed link, they come to page that asks to pick a plan, not the site just created.
Have you looked in the Help section on Managing Users?
You will see that what you described is the expected behavior. When you invite someone to work on your site and they do not already have an Omeka.net account, they must sign up for an account. They can sign up for the free basic plan.
In the future if you have Omeka.net questions, please use the Omeka.net Contact form: http://info.omeka.net/contact