If I need veggies to last I stock up on frozen bags. I know it's a terrible comparison but steamed in the microwave frozen veg is better than going without. That said I feed my pets fresh fruits and veg every day so I try to get stuff to last.
Mangos, papaya, citrus, apples, asian pears, kiwi, pomegranates, cabbage, kohlrabi, leeks, broccoli, cauliflower are all good in the fridge for a while. Just check them, squeeze them, look for spots.
Squash, onion, potatoes, sweet potatoes, garlic goes in baskets on my counter. Keep the onions FAR FAR away from the potatoes. Check often, garlic if it goes will lose it's structure so give it a squeeze, same with onions. Potatoes just start to grow eyes if they get old.
Berries, peaches, regular pears, peppers, plums, green beans, corn are good to freeze and thaw.
I have no luck with cucumber and zucchini in my house. Always goes bad no matter what I do or how I store. I just buy those the night before I need to cook them.