You can really do it either way. I would personally make a custom post type of “Menu Item” then use a custom taxonomy for type of food (e.g., ‘Baskets’, ‘Poboys’, ‘Soups’, etc.). I would then have a custom fields for sizes and price so you could enter something like ‘4pc’ and ’10pc’ and ‘7.99’.
One of things I’ve learned with doing WP sites for clients is that training for the client is often overlooked. Just because you do a great job designing and developing the site does not mean the client will know how to use it. I would recommend taking the time to train your client how to use the site after you implement whatever solution you decide on.
Good luck!