Is this a simultaneous login and then all doing something resource intensive (like take a quiz) or just 60 students may be in there at the same time doing various things?
As Tim pointed out, the main issue with simultaneous logins is a sudden need for lots of RAM by the server, so shared host or underpowered servers may stall at this time, and as Bernard has pointed out in the quiz module takes alot more server resources than the lesson module.
So if your students are going to be logging in at the same time, and taking a quiiz at the same time, you'll probably need a dedicated server with a good deal of RAM from a decent company.
If your students will be accessing asynchronously (60 at a time but not all logging in at the same time) you can probably get away with one of the better plans on your list.
Since this is all happening due to your sysadmins irrational fear of server infecting viruses, the least expensive thing would probably be to get them a class on server administration, which should teach theam a: how servers handle http requests for files and why that doesn't involve file execution on the server, and b: how to install anti-virus software on their servers.