Even password-protected FTP travels across the Internet in the clear. A hacker might not be able to trigger a download without the password. But even that is trivial to sniff.
ssh would be better. But getting non geeks to set that up and configure it would be a problem. Best bet: If you have a server you can configure (like set up FTP accounts, etc.) set up a secure web service (https). That'll encrypt the 'net traffic to slow down the average hacker. And you can apply user ids/passwords to individual subdirectories or trees of subdirectories. Managing these passwords does not require admin permission over the host (like FTP does). Only write permission over your own web share. I'm assuming Apache or something similar. IIS might be a nightmare to configure.