I think there is not standard header size. But a good width for a 1024x768 screen could be from 900-1020. But if you want this header for a public site, you better use something smaller, as there is still users with 800 and less screen resolution!
I always use 980px width for 1024 resolution, but the height is depend what you put on the header, if it has small logo & title text you can use 90-120px, but if it has large logo it'll need more height.
i would recommend designing to fit 800x600. it's small, but you can't really go wrong with it. especially if you design your page to expand automatically.
It is safer to design for 800x600. But it depends on your target visitor. If your visitor is mainly computer geeks then go for a higher resolution.
Yes I understand the need to support a 800x600 visitors. But I have an auto site, so the visitors who are more likely to click on the auto ads are more likely to have bigger screens. I really want to have big picture ads of 250x250, which I think will attract more clicks, and look better on a larger withed screen.