SFTP or SMB depending on your computer/server I guess, or any of the supported cloud options of which there are truly plenty. I'm using SFTP for everything.
FolderSync can do "on-demand" very well if you mean that you just want to tap a sync button to trigger it.
The main reason I use Syncthing is not to use Dropbox for sensitive stuff, which I also use since it's on-demand mobile sync is way better.