That theme component might be a good route, but if you really want to use the pinned banner you can fit a 1050px x 150px image in there without hitting any scrollbars.
Note that as you narrow the browser the image won’t fit, and scroll will return. You can avoid this with a little custom CSS added to your theme to re-scale the image… but the image will start getting really small once you’re down to the size of a mobile device, so it’s not perfect.
#banner img {
width: 100%;
height: auto;
}