Groceries planning based on the sale sheet long cycle looks like this some weeks. Shelf stables and cellar vegetables wait to go on sale. You get enough of them to last until the next one when they do & get perishables and special occasion stuff only when they don't.
Where I am, root vegetables are cheap and readily available above more perishable vegetables, especially when you go by $/calorie. So, for me, it's the obvious choice. And I don't really plan, I just go when I'm out of food and buy what's cheap.
I should clarify a bit further on the potato and carrot thing. Only orange carrots and white potatoes are cheap. There are white potatoes that are called reds and yellows because of the potato skin color. Those are a bit more money. The cheap ones are called russet.
Turtle Island large scale farming. Grains and a small list of produce are relatively reasonable with sales that are a large drop from regular. Only two of them are root vegetables. Potato and carrot. Meat is like this, too. Which meats depends on location. Other food is spendy with few or no sales.