nameauser
Personally, I use KDE's file manager (Dolphin). Plus a curl-cased Bash script for when I need to upload an arbitrary file from one of my home computers via my phone (SSH from phone to computer, sometimes over sat link, run "~/bin/upload.sh /some/file").
I manage my own ownCloud servers (one personal, one company), but hosted options are available.
And yes, it does keep file history (optional, enabled by default), as well as encrypted storage (optional, disabled by default).
Neither the client, nor the server even, require any administrative access.
With that said, on the assumption that it is a way to exchange files between computers and/or share with other users, it would seem to be the case that ownCloud (nextCloud) fits the bill. You can host it yourself (as I do) or use a third party to host it for you. I have been using it for a number of years and I'm entirely happy with it.
Also, depending on your use scenario, another possible option may be https://www.stackfield.com/ a German end-to-end encrypted storage company. I believe there are others offering similar services.