Feel free to point me in a different direction if this isn't the comm for this, but I've been using a corporate cloud service (think Google Drive or OneDrive) to back up my personal files and want to move away from that.
What kind of solutions are out there so that I can back up and access my files securely from multiple platforms (Windows, mobile)? Should I think about setting up a NAS in my home?
well, it's worth thinking about why you want to move off of the corporate service and what your requirements are, as well as what money/time/effort you are willing to put in to get off of it.
Is it a privacy issue? Cost?
If these are irreplaceable files you probably should have backups that exist outside of your home, but if you have a good (ideally, symmetrical) stable home internet connection then a PC at home running something like nextcloud (or a lighter-weight alternative, owncloud ocis is sounding decent?) could handle the day-to-day use, with automatic encrypted backups off on some cheaper, more private cloud service, or on a PC/server somewhere else besides your house.
there's going to be some amount of setup and knowledge required for most good options. You might find it easier to switch to a more privacy-respecting commercial service if that isn't something you have the time/energy for.