Check out VMware Hypervisor.
http://www.vmware.com/uk/products/vsphere-hypervisor/
Installs on pretty much everything and is the backbone to enterprise level infrastructures. It gives you the ability to have it private/internet access (depends on how you configure you firewall). Its fairly simple to setup, all you need is a machine with a NIC that it recognises. It does allow for snapshots, some free backup tools also available. Its extremely small and can install on USB or SD Card. It does just work - even old versions will live on for a very long time.