When I press Alt+PrtSc, it only shoots when I release Alt, so it gets a screenshot of the Global Menu.
How do I get the screenshot of the window without disabling Global Menu?
Installing Shutter would work (as Mitch mentioned in the comments above), but you can also just use the default screenshot program.
One option is to hold down shift+alt, then let go of shift (but still hold alt) and finally hit PrtSc. Holding and letting go of shift prevents the menu or HUD from being invoked.
You can also just set a delay. Type
screenshot into the Dash, then select
Grab the current window with a time delay of your choice. One set, the settings will disappear and you can select the window you want an image of.