In WordPress, you can easily style your menuby adding css classes to each elements and make use of it.
- Go to admin > appearance > menu
- Click on Screen Options (top right of the screen)
- Check the CSS classes options in the “Show advanced menu properties” panel
- add your css classes to the element
Then you can easily style your menu element with the custom css option or in your style.css if using a child theme.
See an example with this snippet : How to add a button in the Customizr menu?