What I should do is create a category group whish should be filled with your "Food Categories". Once you've done that you could display them in your side menu. (If you show the menu on everypage make sure to include it in your _layout.html or as a new block however you like it.
For your food category section.
You could create a Channel for those. Add all the fields you need and put them in there. Don't forget to create a Category field connected to your food categories group. This way you can link an entry to the category it's supposed to go too.
If you created a couple of entries and connected them to their categories. You can display them in the big section by looping over all the entries in your Food Channel. You can grab the category by looping over the category field you made. This way you can add the coloured banner which belongs to the chosen category.
Here are some links for all this:
Craft CMS also has a slack community. For more detailed questions you could ask for help there. You can checkout how to join here.