@MarkSealey: My response is about images in general. Depending on the theme used, and whether it is responsive, there may be other factors at play with a banner.
I always warehouse my images, and then insert with an HTML stack (or a stack that allows warehousing). With the HTML stacks I use this general code:
<img src="URLhere" alt="textdescription" width="100%" />
You can change the width to something other than 100%, but the idea is then the image will adapt to whatever the “container” width is, unlike what happens when I specify a width in pixels.