I suggest you create at least two types website, one for desktop browser and one for mobile browser. For desktop browser i think you might be know that all most all modern browsers have no problem with rendering standard ACID 2 (i didn't know why IE8 keep failing on some sites, since it fully support ACID 2).
Mobile browser generally support HTML 4, and XHTML 1.0 Basic, you may consider what DOCTYPE you will use based on browser support... as far as i create mobile website, i use XHTML 1.0 Basic and WCSS (some sort CSS extension for mobile browser).
So far Opera has been the best on Mobile Browser, followed by IPhone Safari, Pocket IE was the worse and Blackberry browser was too old (except for new devices such as Storm).
Things to avoid usually Javascript and CSS 2 (better stick with CSS 1.x) don't use too much CSS especially positioning & border
And i suggest you to read some article at http://mobiforge.com/
EDIT (add more reference article):
for mobile web design you should check some article like below:
http://mobiforge.com/designing/story/effective-design-multiple-screen-sizes
http://mobiforge.com/designing/story/mobile-app-design-getting-point-part-i