I need help with an interactive web page

Hi - I have a webpage which has a menu with dishes listed and an alphabet letter next to them to show if the dish is a “vegan” dish or “gluten free” etc. Example:
Vegetable pie v
Chocolate cake gf

Down the bottom of the menu I have the key list - v = vegan, gf = gluten free, p=paleo etc

What I want to do is have the key made interactive. So if one wants to see what dishes are vegan and/or gf or low-carb, paleo etc. they can click one or several of these keys and then the menu shows all of the dishes available. They could be coloured or maybe the ones that are not clicked could be greyed out.
Is anyone able to point me in the right direction of how to code this.
Thank you