Hi Sarah,
Fun fact: I lived in Indianapolis for about three years before I moved out west.
Your question seems a bit vague, so I might be misunderstanding here. The size of your header depends on what theme you are using, if you are using an image for your header and if you are hosted on a shared platform like wordpress.com
Most wordpress themes are responsive. That means things like your header will automatically adjust to any screen size including mobile devices. In this case, the display size is largely irrelevant.
A header image that fits the default wordpress theme is 192x740 pixels but this will vary from theme to theme. You can download the default image header that came with your theme to check it's display size before replacing it with an image of the same height and width.
Responsive design eliminates a lot of worries about how much real estate your header takes up on the screen, but if you are using an image be sure to keep the actual file size down to less than 100Kb if possible.
This can quickly devolve into a technical discussion though, as there are many ways to customize and style your header if you are familiar with CSS sheets, etc.
Hope this helps.