So do I create a CSS site that I know looks great in IE, decent viewing in Firefox and hit or miss for the rest? What are the chances with each browser release it will break more and more of my site? Is it worth the time and effort to go the route of heavy CSS pages?
Yes, it is worth the time and effort. Writing your page in XHTML and CSS doesn't mean that it will only work with certain browsers. If you use clean markup and proper CSS, you can achieve a site that looks identical in almost every browser.
New browser releases usually don't have much of an impact on your site design. Often, new browser versions turn out to be more
standards-compliant, so writing your site using strict XHTML and CSS standards should help to maintain cross-broswer compatibility.
If you have the time and resources, rewriting the site from scratch will give you the best results as far as "giving the site a new look and feel." If you're set on just modifying the existing table-based site, you're going to have a much harder time with it.
The big advantage CSS gives you is the ability to keep your presentation/design separate from your content. If you want to make a slight change to your pages, you merely have to edit the appropriate CSS files that determine that style. Down the road, if your boss once again decides that the website needs a new look, your content will still be in tact, and all you'll need is a new stylesheet or two.
The Beer Monocle. Classy.