Winter radishes like daikon and watermelon can be stored in the fridge for many months. Carrots too.
Other roots like beets and turnips for a couple months.
Napa cabbage can also keep for months if the outer leaves are just peeled off for use. Lettuce head storage can also be extended for weeks if the outer leaves are used first.
Sweet potatoes will keep for 6 months at room temperature (60-70 deg).
Loose cut greens should always be used first - salad mix, spinach, baby greens