CSS junky ;)
While I'm a strong advocate of CSS, people here are making a great point that it's not always the answer in all situations.
However, in a situation where you have the time to indulge in CSS, for formatting websites it's what anyone thinking ahead uses. Once you get past the learning curve, CSS is very powerful, flexible, and easier to manage down the road. The only reason I still use tables is for presenting tabular content.
As for your specific image question, someone else already mentioned this but I'll say it again - theme/layout images go in the background, while content related images are generally placed in the HTML.
CSS Zen Garden is a great place to get started!
As for browser compatibility, IE doesn't hold to web standards. You can view browser compatibility and their differences on Wikipedia (Google "comparison of web browsers" it won't let me post a link) ...you will always run into discrepancies between browsers. And honestly, most sites look great in all browsers except IE.