Stylish and functional, I'd suggest you take a look at lifehacker.com . Functionality wise, it depends on what's appropiate for the type of website. There's a reason why portal websites are rarely being used (except on say, company intranets). Stylish I would attribute to a lot of things including layout, conciseness, typography, certain interactivity, considerate and a few others including things like support for graceful degradation where appropiate.
A website in my eyes is something someone visits with predetermined intentions looking to satisfy themselves within a specific niche. This described behavior doesn't differ from real world examples such as when you go to a supermarket to buy food.
http://www.quora.com/What-startup-homepages-are-most-simple-...