I love using my keyboard for most tasks, and use the Windows Key quite frequently to start programs, or do things such as Windows+R to get the Run prompt, etc. Is there a key combination I can hit that mimics the Windows Key press when my Remote Desktop (windowed) session has focus? Just hitting the key triggers it in my primary OS, not the Remote Desktop session.
First... if you are fullscreen in your session, the Windows key works like you would expect on the remote computer. So, you are talking about if you have the remote session in a window, and not fullscreen.
But, if BEFORE you hit the Connect button on the Remote Desktop Client, you click the Options button, and then hit the Local Resources tab, you can there decide where to apply the Windows key combinations. Specifically, in FUll Screen, on the local machine, or on the Remote Machine. Microsoft did appear to take the Windows Key into specific consideration here. Why? Because of exactly what you mention.
So, you set that option to be Remote Machine, and then connect. Whenever you minimize the remote window, the Windows key works on the local machine like it should.
Alt + Home will display the Windows Start Menu.
Here is a page listing more keyboard shortcuts while on your remote machine: