If you plan on sharing files that will be on more than one hard drive, then an FTP server would probably be the best and easiest way, or that's my guess. The problem with using something like Joomla is everything has to be either in the root directory or sub directory of your web server as far as I know.
I don't know how you link to files outside this range. Plus, with an FTP server, you wouldn't have to design or keep updating the content when you added or modified your files. The only drawback to FTP though is it's lack of security. I recently did some reading on that and it seems like there are some things you can do to greatly increase your security, but I"m not sure how much.
Now as far as Filezilla copying files, that doesn't sound right at all. The Filezilla FTP Server software just acts as a portal allowing you to make a connection and access content in the assigned directories. I wrote a tutorial on how to properly configure it if you want to take a look:http://www.myownserver.info/index.php/step3-installing-components/7-installfilezillaftpserver.html
There's a footnote with some info on FTP security and a good link to another site detailing it better.
Filezilla FTP Server is actually quite easy to setup and configure.
Oh, and by the way, I have a private section on one of my forums that I've used to organize and share files with. Since I only want to share them with people I choose, I've set the permissions to where I have to give them access to that area, otherwise they never know it's there. It's a great and easy way to quickly organize and even categorize content. Plus, it doesn't have the security issues of the whole FTP thing.
That might be something to consider.
I hope that helps.