The only fatty fruits/vegetables I can think of are olives, avocados, and coconuts. And of course, olive oil and avocados are both great sources of healthy monounsaturated fat. Coconut is of course full of saturated fat and should be consumed in moderation, but its saturated fatty acids are supposedly shorter chain than, say, butter or beef. So I wouldn't even avoid coconut completely. I just would not consume too much of it.
Some fruits/vegetables have little in the way of nutrition, such as iceberg lettuce. They might help you feel full on fewer Calories, and they might provide some of the fiber you need, but there are certainly better choices out there, such as romaine lettuce, spinach, or swiss chard. Some fruits and vegetables also have lots of carbs. But pretty much all of them are reasonably healthy so long as you don't deep-fry them.
Some foods, such as onions and tomatoes, supposedly are healthier when they are somewhat cooked than when they are raw. Many though, such as green vegetables, have nutrients that are damaged by heat. With such vegetables, it's better to gently steam them, through them into a stir-fry near the end, or not cook them at all.
Fibrous greens are great because they will keep you feeling full while barely eating any calories..asparagus,cabbage,brusselsprouts.
I would watch how many fruits you take in the though, because the Fructose in them can get pretty high. Look into kiwis,mandarins,blueberrys.
Kiwis have the most vit c and vit e out of any fruit, and has lots of antioxidants and is the worlds best natural blood thinner