As others already suggested, if you already have a Windows Server license, you thus have an enterprise-grade virtualization platform in your possession. If it is a Standard edition, then you can use it this way:
(1) install one instance of Windows Server on a physical server with up to two physical sockets (number of cores doesn't matter, matter processor sockets, so your server qualifies), this is called "virtualization host"; you can not install any other so-called "roles" (DNS, DHCP etc.) of the OS except the Hyper-V role on this instance.
(2) you can install up to two instances of "guest" Windows Server operating systems inside your "host" system. Install any roles you want on these instances.
(3) install any number of Linux guests inside your Hyper-V host; that is, the number of virtual machines is not limited by the licensing restrictions, only the number of Windows guests is limited.
As to the free Hyper-V server, it has been cumbersome to manage it in a non-domain (that is, workgroup) environment, so you would need another full-featured Windows Server (at least two, actually) serving as (a) domain controller(s) to manage your Windows-based hosts, including those with the free Hyper-V Server installed.
Do not forget to consider Storage Pools, a RAID-like software technology built into newest Windows versions. It can give amazing performance even on traditional HDDs. Using direct disk access for virtual machines is not that necessary, nor recommended.
As to the Linux guest support, it has been significantly improved in the latest versions of Hyper-V, but still there is room for improvement; there are multiple articles from Microsoft on how to configure Linux guests in Hyper-V.
- EDIT (in response to the comment below):
No, I meant "normal" Windows Server 2012 R2 – either Standard or Enterprise (they differ mainly in licensing – Enterprise doesn't limit Windows Server guest instances, Standard limits them to two, but you can install more guests having additional licenses; I suppose you have Standard edition).
When I started using Windows Hyper-V Server (which was free from the beginning) it was 2008 version, then 2008 R2, and this was cumbersome in a workgroup, although not impossible. I simply don't know if things have changed with newer versions of the free Hyper-V (because currently we run Standard edition), but I suspect they have not. To form up the picture, look here: http://blogs.msdn.com/b/virtual_pc_guy/archive/2010/11/11/configuring-remote-management-of-hyper-v-server-in-a-workgroup.aspx and here: http://blogs.technet.com/b/jhoward/archive/2008/11/14/configure-hyper-v-remote-management-in-seconds.aspx and google for 'hyper-v workgroup' to find more.
So, just install your full-featured Windows Server 2012 R2 on your hardware (Tip: don't enter the product key when installing, you will be able to activate your installation later; first test the configuration, then activate it, if satisfied); install drivers, configure network, storage (explore Storage Pools); then install just the Hyper-V role. This role by default also installs management tools, i.e. Hyper-V Manager – use it to create and configure virtual machines. You can install two instances of Windows Server 2012 R2 as guest systems (they will also require activation). For example, configure one instance as an infrastructure server (DNS, DHCP, even DC) and use the second to host your Windows application which you mentioned. Then add *nix virtual machines; read this article: https://technet.microsoft.com/en-us/library/dn531030.aspx and use Google for more information.
This configuration is actually a workgroup configuration too, because there is no domain controller or at least the Hyper-V host is not joined to a domain. But this does not matter because now you have management tools installed locally on the virtualization host; you will also be able to connect from your workstation by RDP and thus use Hyper-V manager kinda remotely. But if you try to install Remote Server Administration Tools for Windows 8.1 https://www.microsoft.com/en-US/download/details.aspx?id=39296 on your workstation, you will face the same problem as with the free Hyper-V. So the point is this: free Hyper-V does not have local GUI and requires purely remote management, which is difficult to configure in a workgroup; in contrast, full-featured Windows Server 2012 R2 permits you to easily manage your Hyper-V role simply because there is a GUI installed locally and accessible both locally and remotely – via RDP (it's also possible to install some sort of VNC).
To complete the picture: although free Hyper-V doesn't have its own GUI (all it has is an empty desktop with command-line windows and restricted text-based management tools) there are 3d-party tools, including free versions, that permit you to simulate full-featured Hyper-V host, for example: http://www.5nine.com/5nine-manager-for-hyper-v-free.aspx But the initial configuration (network settings, enabling RDP) still needs to be done manually. You will also have difficulties dealing with uninstalling programs (no Control Panel), Windows Updates, etc...