Many linux distributions do not require you to install a GUI. Debian and Ubuntu both have this capability to name just a couple. If you install Ubuntu's server version, or uncheck the Desktop environment and check SSH Server in Debian, you'll be able to manage your Linux server like you're managing your AWS instance.
You need linux installed or running off a live CD if you're going to use it as a server. If you don't want to overwrite your desktop installation, you could always use a virtual machine. VirtualBox is a good virtualization software for Windows.