Libraries are good for production, but not for learning
I've worked in AJAX land for just over 2 years. Over those 2 years I have come so close to the DOM that I sometimes have dreams about it. I created a couple libraries that helped me pretty significantly in cutting down some code and cross browser deficiencies.
But now, over the past couple months I have come in tune with jQuery. I've let my inhibitions loose and am diving in. My libraries were great and all but the fact that jQuery has a full time team working on it and strong community support I can't help but give in to the fact that it saves me time. The overhead of keeping my own library stable, standards compliant, and new features being added are just too much.
So for all you DOM scripting, AJAX beginners, here is a good path to go down:
1. Spend a couple months not even thinking about a library, just using standard DOM scripting on your sites (you'll be much more grateful when you start using a library like jQuery to see how many less lines you have to write).
2. Think about some ways to cut down the code yourself, consolidate it, make it reusable(creating your own mini library).
3. Understand that you can't do everything yourself. Realize the benefits you will have from using a widely prevelant library like jQuery.