Never use alerts to output debug info - the alert itself may interfere with the events you are trying to debug
console.log is mostly reliable - but sometimes the value of a variable will not be what you think due to firebug weirdness (or hoisting?) - use break points instead.
If you are required to make stuff work in IE the JS debugger that comes with IE8+ is actually rather good (and more stable than Firebug).
JS Lint your code but don't use an overly zealous settings. JS is flexible - no need to constrain yourself.
Crockfords good parts is mostly about his general preferences for programming style. Definitely don't read it like the bible.
If you want to focus on UI learn how to use events properly - this means not using frameworks but doing it from scratch yourself.
Read up on event driven programming and asynchronous behaviors
Learn JS first - then jQuery, Prototype, whatever second.
BTW Using PHPStorm on Win7 64