I don't think you can go wrong with Firefox or IE8. Chrome and Safari are a little less stable and web developers test less for them.
IE used to be a web developer's nightmare, but Microsoft has made massive improvements since IE6. I find that IE8 is much better than Firefox when it comes to flash content (e.g. youtube videos).
Firefox is fantastic for web development because it has some very useful plugins (e.g. Firebug). I think it renders web pages a little better than IE, but the gap has become very small with IE8.
BTW, there's nothing to stop you installing *both* Firefox and IE and trying them out. The differences are small enough that it will come down to personal preference.
Full disclosure: I worked at Microsoft for quite a few years and I know people who work(ed) on the IE team, but due to the development environments I use these days I spend most of my time on a Mac in Firefox and Safari.