You want to set up a PC\server\host with a Hypervisor running a number of VM's and also have one of those VM's act as the console operating system for that host. This is the sort of thing that a Type-1 Client Hypervisor is supposed to deliver.
Unfortunately there aren't any mature mainstream examples yet but Citrix can now deliver a Type 1 Client Hypervisor with the XenClient component of their XenDesktop solution. VMware don't have one despite a lot of rumours over the years, and recently they have indicated they don't have anything ready to release. Some other companies (like Virtual Computer with their NXTop product) can also do this but they are not very well known.
In any case you are looking for a product that is described as a bare metal or type 1 client hypervisor, and sometimes it's called a bare metal desktop hypervisor. Common virtualization solutions generally fall into the Type 2 hypervisor bucket (VMware Workstation, Fusion, Parallels, VMware Server, Virtualbox..) or the Type 1 server hypervisor bucket (VMware ESX\ESXi, HyperV, Xen). Even if you plan to run a Server OS on this system what you describe requires a Client Hypervisor, at least as far as the major virtualization vendors use of the terminology is concerned.
The second thing you want to do is have a minimally configured other PC that automatically connects to a VM instance on the first system when it boots. There are a ton of solutions for this - search for Thin Client LiveCD for a bunch of examples e.g. ThinStation.