UK Education Data protection policy's and security information needed to show Head Teacher

For the first part, have a look at the https://www.microsoft.com/en-us/trustcenter/cloudservices/office365, which covers some related topics.

For migrating data to SharePoint, that needs to be done with a lot of thought and planning.  For that amount of data, a migration tool would be recommended.  You need an https://channel9.msdn.com/Events/Ignite/2015/BRK3190 and https://support.office.com/en-gb/article/Overview-best-practices-for-managing-how-people-use-your-team-site-95e83c3d-e1b0-4aae-9d08-e94dcaa4942e for starters.

Have a look at what https://fasttrack.microsoft.com/office offers, if you are eligible it comes with benefits like data migration help - https://technet.microsoft.com/en-gb/library/office-365-onboarding-benefit-process.aspx. Here is another article that may be https://practical365.com/clients/onedrive/migrate-home-drives-to-onedrive-for-business/.

Though not a recent article check out this article which has some helpful steps - https://blogs.technet.microsoft.com/ptsblog/2013/11/04/migrating-file-shares-to-sharepoint-online/.  Be aware you may come across a https://support.office.com/en-gb/article/Manage-large-lists-and-libraries-in-SharePoint-b8588dae-9387-48c2-9248-c24122f07c59 of 5,000 items as well, though that might be improving and if you get your IA right, you shouldn't hit this limit.