You’re on the approach; you’re looking for responsive design. That means design your site for mobile users first. One of the basic designs is to have menus drop down with a hamburger icon.
All drop downs are the same, you can only code the HTML in so many ways
It’s the CSS that makes the difference.
Many websites use Bootstrap. Look for components and check out the different options. Their code can give you an idea on many options.
One thing I can say is I see you using media queries; are you familiar with them?