[Disclaimer: i am the developper of SDL]
Since you have personal computers in the lab, i do not see the benefit to concentrate the computations of all the students on a huge server, it is far lighter to let each personal computer of the lab do the computation asked by the student in front of that computer (and if some student runs a stupid loop that eats all the memory, the other won't even notice it).
Since you are in touch with the IT crew of you university, you could think about:
installing a GNU/Linux distro instead (resp. aside) of Windows, and then use Sage from there.
install Sage in Windows with the recent cygwin build (https://github.com/sagemath/sage-wind...) but you will not be able to benefit from the many optional packages provided by Sage.
If such things are not possible, an alternative could be to use the SDL
(https://sagedebianlive.metelu.net/), which is a live-USB containing Sage (with
most optional and experimental package) and other tools (e.g. LaTeX, R,...). The official images are available on Sage mirrors.
Pros:
easy to deploy : start from one key and clone it from key to key ; since
each cloned drive becomes a new seeder, you get exponential replication
speed.
no need to install anything the lab's computers nor on the student's laptop
every student has the same set of available software (compilers,
editors,...), no problems related to differences between versions.
students can use Sage at home, and even keep their data between the
classroom and their laptop since SDL allows persistence of the home/
directory between boots.
the build system being modular and open, you can compile your own custom
image with exactly the software you want (do not hesitate to ask me if you
need help or would like to see some interesting packages entering the next
official versions).
Cons:
each student have to buy a >= 8GB USB drive (this could also be provided
by the university, or you could decide that the USB drives must stay in the classroom).
windows 10 might hinder access to the BIOS to allow booting from the USB drive
(so-called "secure boot" and similar crap). On the computers provided by
the university, the "unlock" operation could be run only once.
I have had feedbacks from teachers in Spain and France universities about
successfully using this method for a whole class couse, as well as feedback from
various countries about using this during Sage workshops (up to 2 weeks).
Note that SDL with Sage-8.0 is going to be released soon (migration to Debian
stretch takes some time).
Do not hesitate to give feedback about your experience and what leads to your final choice.