I know it seems a simple question, but when I make my images the size of the sample header, some of the image gets cut off at the right of the screen...

see: www.RussellKansasHistory.org

And yet, if I don't make them wide enough, I get some images sticking out on the right...(cache issue, I think...but not sure)

So what does size does the header need to be? Width wise?

It depends on how wide you set your site width.