It's a common question for many of my customers who I have helped to migrated their on premises Tfs instance to Visual Studio Team Services using the TfsMigrator tool from Microsoft.
I have procured a few items that are most common in my experience post migrating to VSTS. If you have any you'd like to share, please feel free to leave a comment for everyone else to peruse.
Validate Users, Work Items, and Source Repositories
Update and run builds and releases
Hope this is helpful in your quest to VSTS. Cheers!