What Pipedrive user role should I have for successful migration?

Your Pipedrive user role doesn't matter.

But keep in mind that to migrate automatically all data with no exceptions from Pipedrive you have to fill in API keys for every user in Migration Wizard.

If not, only a part of the records will be transferred. To be exact, the service will move automatically only those Emails and Attachments that are related to the user/users who's API key was/were entered for the transfer.

So, do not forget to enter API keys for every Pipedrive user you wish to migrate.