header size

Lets say I create a Header image that I want to be contained with a Menu showing below the header media.

Is there a good choice from amongst the layout options – minimal, medium, etc.

If I go with an image that is 2000×1200 it seems too tall to fit.

What is the ideal combo of image size with layout so it can stretch to the full browser width and yet look good on mobile with menu after the header media on desktop?

See http://jldiscovery.com/

I had to add 300px padding to move the menu down far enough 😉