Some users may be running low resolutions like 800x600, so you should try to make it fit for them (or have a low res style for them). I think the image size fits nicely at 780px. The highest you should go is around 1000px, 1179 is definitely pushing it.
If you want it to be fullscreen with a lower banner, make 1 or 2 edges of it repeat so you can apply a background to get the full screen effect (this site does it nicely, as do many others).
If you select all, you can see where the images end and the backgrounds begin.