I read that vCenter should be installed on a Windows system (I'm not sure what version of vCenterwe're getting; I suspect it's 6.7) and it can't be installed directly under ESXi
No, that's not accurate. Windows vCenter is dead after 6.7 and should not be deployed. Use of the appliance should be the only path.
So, to that end, we are also installing another real system with Windows 2016 Server.
This would be a total waste of a Windows Server license and a physical machine. See the above comment. The vCenter Server Appliance (vCSA) is what should be deployed in your environment, which runs as a VM on one of these ESXi hosts. This is how it's done.