I would like to develop a site using jQuery that will work with all major browsers. I thought to start with a basic layout (a header, a couple of tabs with content, and footer).
jQuery itself cant help you do this. You have to get the hang of basic HTML and CSS. Use Javascript and jQuery if you need it, don't use it just to use it. You should work with pixels or percents when it comes to dimensions on the web. Points are for printing. Font sizes should be set in EMs or pixels.
A fixed layout is the most common for normal web pages, and by using grid frameworks like 960gs, you have an easy way making gthe proportions look decent while still supporting the vast majority of screen resolutions. It's also far, far easier adapting graphics to a fixed width layout, and at the same time make the page easy to use.
Keep in mind when/if using percentages that text lines longer than about 600-800 pixels is difficult or slow to read. Aka having a content area of 80% could be a nice idea for a viewport that's 1000px wide, but if you have a viewport of 1900px, the site becomes mostly unusable.
And one usually does not explicitly set a height on things, as the height will automatically increase as the content of the container increases. Of course, you can set the height on certain things, but it all depends on what, really.
So, using a dynamic or fixed width all depends on your content.