Some things to beware of when replacing shared areas with sharepoint:
1. Sharepoint isn't really the best document management system, and from my experience you will face a lot of resistance to its use. The fact you have to go through O365 was a particular point of contention for my staff.
2. Don't just map your shared area to a document library, you waste 99% of the functionality of sharepoint (also, you will very quickly hit the file limit for a document library). Instead, chunk it all out. I had the curriculum teams sort their documents out (e.g maths, science so on) and then provide them with their own sharepoint site to store it in. This will also allow them to sync the materials useful to them without syncing every last file (RIP your network!)
3. Once this chunking task was completed, using file explorer/mapping network drives allowed me to upload folder structures without hassle. To fufill the auto login issue, go to the page you wish to use file explorer for, copy the url, then log out. Paste the url back in and login through there making sure to tick the keep me signed in box as you go in. It's temperamental as anything could be so you have my sympathy for this.
It's a herculean task to be sure, and what summers were made for. sadly, some heads think its a simple copy/paste!