One possible layout
On desktop, opt for a header with 2 or 3 rows. Due to less restrictive space requirements, you should surround major icons like the search box and shopping cart with a whitespace so they stand out more prominently.
There are various possible layouts, but below is a draft mockup of one of them:
- Contact info
- Free shipping mention (it could be moved to the left)
- “Help” link
- Country selection
- Logo (clickable)
- Search box (prominent, especially on the homepage)
- Account icon
- Cart icon
- Mega menu with the main categories as the level 1
A variation on the layout above
- separated top bar for the free shipping and help link
- no country
- labels on the icons
- added the opening hours
- moved the phone number
- highlighted Specials menu item
How tall should the header be?
I looked at 12 well-known brands, and the average is 21.5% (measured with a browser ‘real estate’ of 1247px tall). I’d recommend keeping it below 20%.
Hyperlink the elements in the promo bar
What I like in the promo/announcement bar in the image below (Cotton Mills), above the menu bar, is that the 3 unique selling ‘bullets’ are clickable. It allows shoppers to quickly get more information by clicking directly on those.