«для»(for) always takes Genitive nouns
Food offers a delicious intake of mass nouns. Russian has them massed up even where English does not!
The formal word for potato is карто́фель (German speakers, rejoice), but it's hardly ever used in speech. Use «карто́шка» instead.
The word for tomato is помидо́р. There is also the word тома́т, but it is
the base stem for derivative products: тома́тная па́ста = tomato paste
посуда is a word for different containers used for cooking , consuming and further storage of food. English, sadly, does not have the exact equivalent. However, it is obviously "dishes" that you wash and "cookware/tableware" that you buy.
In this skill, we used perfective verbs for "cook", "cut", "wash". The reason is simple: that's the verb you'd use when you want a single specific action, often with a result—rather than referring to "activity" (activity may be fun but, in some cases, pointless).
More on that later. For now, just go with the flow.