Since you need to get virtualization for free, VMware vSphere Hypervisor is not an option. That being said, VMware vSphere Free edition would not provide any beneficial features like erasure coding, clustering, HA and FT, DFS or VSAN due to license restrictions.
I would suggest you look at Windows Server Hyper-V Free 2016. It does not have GUI, however, provides you fully functional hypervisor for free with built-in features such as ReFS and nested virtualization.
As a shared storage provider either HPE VSA (free) or StarWind Virtual SAN can be used providing to Hyper-V Cluster highly available and fault tolerant storage presenting local disks as iSCSI ones. Personally, I would prefer StarWind so far it's native for Windows and provides significant storage performance due to the usage of built-in RAM and SSD cache features.