ESXi. Its free, powerful, and offers a lot of pre-built appliances. I don't see any safety concerns if the network is segregated. If you have specific VM's that you want the students to learn within, keep screenshots of those so that you may roll anything back that gets damaged. This is great because it allows them do pretty much anything they want without creating a maintenance headache for you.
If you want to teach them about specific technologies using VMs that go hand and hand with programming (like source control, bugzilla, configuring web servers, etc), turnkeylinux.org offers many free linux appliances that will make your job easy.