How would I make a keyboard shortcut to *maximize* the current window?
One of the easiest ways to do this is to use BetterTouchTool. It will let you bind a keyboard shortcut or a trackpad shortcut to many commands, including maximize window.

Once you are in the BTT settings page, do the following:


Go to the Keyboard tab on top.
On the bottom near Keyboard shortcut, enter in whichever keyboard shortcut you want.
For Predefined action, choose Maximize Window.


There are many other options related to maximizing besides "Maximize Window":


Maximize Window Left
Maximize Window Right
Maximize Window To Bottom Half
Maximize Window To Top Half
Maximize To Next Monitor