Categories Buttons and Filters Oh My

Ok so I am curious how this would work.

I want to provide a tool to find food within a wordpress site by filtering through posts that have certain categories and tags attached to them. For example let’s take Bobs Seafood, I would create a new post for Bob’s Seafood on my wordpress site, this would be his restaurant’s profile page on my site. For categories, I would make sure “Sea Food” “Dinner” “Lunch” were marked on his profile.

Now, on my site’s home page, The user is asked “Are you looking for breakfast, Dinner, or Lunch?” and has 3 buttons to choose from. Let’s say the user chooses Dinner.”

The next screen shows different categories of food, all of which are buttons, the user chooses seafood.

Now I want the results to reflect the choices he’s made on the home page menus and display restaurants that have BOTH “dinner” and “seafood” as categories. My question is, how do I display a blog page that only shows results (posts that have the categories specified by the user in the beginning menues)?

Any help would be GREATLY appreciated. I plan on having an extensive amount of categories and eventually want to be able to prioritize the placement of posts that pop up during the final results after a user inputs their selections.