Keyboard, notification, or menubar shortcut to compose mail message?
Solution 1:
The easiest way out-of-the box is to use the "services menu". Just select some text anywhere (a single character will do), right click to open the context menu and select the bottom-most item "Email Selection":
If it is not present (should be) you need to enable it under System settings -> Keyboard -> Keyboard commands -> Services -> Text
Solution 2:
Mail Unread Menu is what you want. Free/donation-ware. Compose New Mail from the menubar.
Also custom alerts and more. Working well in Mountain Lion.