Depends on how big you want the header image – it can be tiny or really big, it all has to do with your design.
If you want it to span the entire width of your page, it should be around 1500px I’d say.
For the background image, I suggest using images that don’t have any text etc.. as it won’t show on all screens due to aspect ratio changes. Background images should be designs/patterns, and again can be as large or a small as your design needs ๐