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Nandita,
One of the key factors to keep in mind in planning an O365 deployment is user adoption. The technical part is "almost" straightforward, but if you don't get the users on board, it will fail.
The best approach is to define adoption groups, for example, by department. Each department will have different needs and pain points, and thus, possibly, different priorities. Get champions engaged from each department to help understand a unit.
Technically, you can turn on a number of things at once, but others, you should do in a more structured fashion.
In my last organization, we did turn on licenses for everyone early on, to encourage grass-roots adoption, while running deployment streams in parallel. We also ensured we, as a project team, used as many of the features of Office 365 as possible. For example, we provided updates through Yammer, collected feedback using Forms, and automated ad-hoc requests through Flow. We also created a knowledge portal using SharePoint Online.
Technically, you have a couple of main migration items to look at:
- Mailbox migration: this can be phased, however, while Microsoft has been improving the technical capabilities, shared mailboxes can prove to be a complication. It is best to migrate users as a group, including their shared mailboxes and shared calendars.
- OneDrive: the best is to try to get users to migrate their data
- SPO: beware of trying as-is migrations of network data or existing SharePoint sites. Many organisations, in my experience, are not good at housekeeping, and you could be migrating a lot of old data that could be archived instead.
In terms of getting users engaged, focus on the products that are differentiators:
- Teams for collaboration
- Flow for workflow processing
- Forms for surveys and feedback
- PowerApps for your customized application needs
For me, the bigger mailbox, the big "network drive" and plenty of SPO space are now background items, not the selling points of O365
Ivo