This answer refers to a Splash Portal created with "classical" templates, and not based on layouts such as Metro, Hospitality etc.
Firstly, the image should not be greater than 500 KB.
This helps avoid problems uploading the image and ensures a fluid end-user experience into the Splash Portal.
Regarding the width and the height, please note that the image is resized according to the width of the browser: for this reason it is recommended to upload large images (about 1160px width), in order to ensure a good quality for all screen resolutions.
To create a background image for the header of a Splash Portal, please read Setting appearance, languages and public URLs for your Splash Portal.