We use the AvePoint DocAve (now called Fly) for file migrations. Available from TechSoup for $343 for 250 Gb of data movement (though AvePoint has been very generous to us and allowed us to move much more data than this when we've asked).
I've hired Peter to help me with this very project. So far he's done pretty darn good work. :-)
That is great that you already completed the file clean up. That is always a good place to start. To add to the previous suggestions, here are some other considerations:
While not specific to SharePoint, here are some general guidelines we published on moving to cloud-based storage: https://www.delcor.com/resources/blog/what-you-need-to-know-before-moving-to-cloud-file-storage
Hope that helps!