Early potatoes will store for about five days in a cool, dark environment. Keeping them in hessian bags will allow the moisture to escape and is ideal. Plastic bags do not do this! Only keep undamaged and healthy looking tubers to avoid infection which could spread to a whole batch, making them unusable. Usually it is best to only dig your potatoes from the ground as you want to use them. Maincrop potatoes which are harvested later which usually store the longest.
Broad beans will keep in the fridge for up to five days if you are going to use them in that time. To make sure that your crop is not wasted, freezing is a very good option. Pick and pod your crop, then cook in boiling water for about one minute before putting them in ice-cold water (known as blanching). After this remove the beans from the water, dry them as much as possible and seal in an air-tight container before freezing. They will last for at least six months frozen, making delicious broad beans available during the winter.
Courgettes (Zucchini) are always best eaten fresh, but can be stored in the salad tray of the fridge for up to about five days. It is usually treated as a vegetable, but it is botanically a fruit! Pickling them in vinegar, if you like the taste, or making a piccalilli and sealing in an air-tight jar will preserve them for longer. If you leave courgettes on the plant for longer they turn into marrows (Summer squash) which have a different flavour. As marrows they will store for longer.