Hi New2dieting, and welcome!
I saw your post on another board I think. You are quite small and right now you're limited as to what sort of exercise you can do, right? I think you said you were aiming for about 1060 calories because of your size? But always hungry?
A common concept on 3FC (that I agree with) is that diet is more important than exercise. It's so easy to out-eat an exercise program. However, I think for people who are small and don't have a lot of weight to lose, their calorie requirement is already pretty low, and exercise is very important to give them a little more wiggle room with calories.
Do you have access to a nutritionist, or someone knowledgeable who could help you come up with an eating plan that packs a lot of nutrients into such a small allotment of calories?
Does your physical therapist have any suggestions regarding exercise you could do? Can you pedal a bike, or even one of those little pedal-only contraptions you use while sitting in a chair? Or can you use an arm-cycle? Heck, on the Biggest Loser they had a guy who was injured and he would sit on the bed and shadow-box. This woman has a lot of different "bed" workouts:
Laurel House Quickie Fat-burning Bed Workout. Can you lift weights, even just hand weights? Building muscle is great for weight loss.
My sister is disabled and only 5 feet tall, and she lost a good amount of weight with Weight Watchers and has kept it off.
To answer your specific questions:
Diet or exercise: For me, diet is key. I can out-eat my workout with one stop at Starbucks.
Specific diet: I count calories, but I find I'm more successful if I focus on fruits & veggies, lean protein, yogurt, cottage cheese. And veggies. And veggies. And veggies.
How much do I work out: I run 4-6 miles 4x/week. Used to run more before injury, just getting back after a couple months.
Calories: I lose on 1600/day. Would probably lose pretty well on 1800.
Hope this helps... good luck!
What works for you?
I've been heavy all my life, so I've tried many different diets. We have been doing a weight loss challenge at work and my supervisor, who has never had an issue with weight until recently, is doing fabulous on weight watchers. She doesn't go to meetings. She borrowed my startup kit and downloaded a couple of free apps on her phone. One with a scanner, one is a points tracker and then a points calculator. For someone who has never really dieted before she sure is kicking butt. I don't think she's had a week yet (started June 14th) where she hasn't at least lost a pound. She also walks almost daily, a really brisk walk. 
