Comment Use a VM (Score 1) 261
Like others mention, use a virtual machine like VirtualBox, and give everyone a virtual machine of your Linux system in addition to instructions to set up their own. This will save countless hours of helping your students get up and running.
To your question, what distro? I'd recommend Centos, which is a free as in beer version of Red Hat Enterprise Linux (RHEL) and/or Oracle Enterprise Linux (OEL). The only real differences between the three is branding and the support contract, with a five year support plan. Both Red Hat and Oracle have a Linux certification test, if you are looking to have a 'real' certificate when they are done.