Sorry, the APIs are a bit confusing since they were only designed with our web app in mind so they kind of grew organically. The call that you want is /api/v3/users/initial_load. It returns all the data that our web client absolutely needs to render including the current user, their teams, some user settings, and configuration data.
And regarding your authentication error, you should be setting the "Authorization: Bearer Token" to header to the value of the "Token" header received when first logging in. That should let you access all the APIs.