I'm a little leery of recommending anything, given your characterizations of the intended users beng "Computer Stupid", as those guys can break "anything", and I wouldn't want to get blamed!
That said, there are a lot of "filemanagers" out there, but I can think of none off hand that allow you to limit disk space. You might dig around hotscripts.com, and see if one of those (newer?) ones has that feature. It also is important to know what kind/size of files they are gonna want to be uploading, as "big" files (over 7 MB) like video and some hi-res photos are going to be problematic for PHP based stuff, given the upload size limitations.
I suggest you check out the "free" version EasyHost. It has worked very well for me for similar purposes. It doesn't have the file upload size problem, lets you segregate users' spaces, allows for easy management of individual logins for the users, lets you control the types of files accepted, and lets you limit space used (you can see the fulll ist of features here). Additionally, since it is perl running cgi, it runs as your user on DH making subsequent handling of the uploaded files really easy. The "commercial version" is considerably more powerful and is not that expensive, but may well be "overkill" for what you need it to do.