What is best to eat for avoiding cancer
Michael Pollan has a great suggestion: don't eat anything that your grandmother wouldn't recognize as food. (apologies if I've made the wrong attribution)
For a much deeper appreciation of cancer and carcinogens: Emperor of all Maladies: A biography of Cancer by Siddhartha Mukherjee. It won the Pulitzer Prize for its exquisite writing and compelling narrative. The takeaway is that many complex factors can contribute to cancer.
I don't think there is an easy answer for this. There are many recommendations depending on the type of cancer you are concerned about. In general, eating foods that are processed as little as possible is a good idea. Organic is wonderful, if you can get (and afford) it. As a surviver myself, it's always a balance deciding what to put in my body, how to deal with stress, getting enough sleep, exercise, etc.
All of the above plus my doctor strongly recommends blueberries, cherries and cranberry juice,
Another piece of advice I have heard: don't eat anything that lists an ingredient that an 8 year old can't pronounce.
"Eat your colors" is another catch phrase I've heard. Foods appear in a wide range of colors, and the colors are the visual indication of healthy protective properties. There has been much research and not all of it agrees, but simple principles work -- moderation, variety, quality. I would recommend Meg Wolf's website, www.becomingwhole2.com, and her books (check the site).
I'd be more concerned about packing...using plastics in food containers, bottled water, foam, etc..etc.
Along with other items in your household, cleaners, disinfectants, insecticides..etc.
that said: broccoli, carrots, cabbage, Brussels sprouts have antioxidant and cancer fighting properties.