You need to make sure that Windows Firewall is not blocking you ports.
if you still want to build a new computer just for minecraft you need to use what ever OS is best for you.
Linux is great for dedicated server because you do not have hundreds of services running waiting CPU time and Memory. But it's a pain in the ass to set up right if you do not know what you are doing. Windows server editions are middle ground. Not overly hard to set up, but still more work than a simple install of Windows 7. For most people Windows 7 is the way to go since it's what people are used to using on a day to day basis, but it will limit your resources for your server instal on older machines.
Just what ever OS you go with you are going to want to be sure it's a 64bit version, with a 64bit install of Java7, to even use that 16gb of RAM you plan on putting in it.