All browsers have their various quirks and no browser is guaranteed to display or act the same as another. While W3C is making great strides to expand the functionality that should be standardized, many RFCs are not yet to the Recommendation stage, which is the stage that means it will no longer change and are more likely to be acceptable standards to develop on. Because of this, it is imperative that you ensure your site works in, at minimum, the browsers within your focus group
First, use reset.css. As the page describes, it does a pretty good job of resetting all elements to the standard display format. While not perfect, it gets pretty darn close in all browsers, which is more than you can say without it.
Second, check out QuirksMode to see the various browser compatability with standards (whether those standards are in recommended stage or not). This is where you can decide on the features you will use that match the compatibility with your focus group.
Third, assuming you are on windows (or have a VPC image of it), I recommend installing IE8. Also, check out IE Tester, and install the DebugBar for it (but disable it in IE8), to give you the ability to validate and debug your code in IE 5.5 through IE7. Install any other browsers that you consider in your focus group. Doing so will allow you to test, without question, the appearance on the page.
Using these tools you should be more than able to develop a design that will look 99.9% the same in any browser that supports the features you implement and validate that it is implemented correctly. While it can be a bit daunting, this will greatly reduce the chance of display/js related bug upon release.