I would recommend using as little outside support as possible. The point of stability exercises is to train your body to do the stabilizing and using outside support could become a crutch you won't be able to get away from. Instead of using walls and furniture and whatever to keep the ball still, why not try some of these techniques that will challenge your balance and get you stronger:
1) deflate your ball a bit. This will make the bottom and top and bit flatter, and it will be less apt to roll. As you improve, you can add more air.
2) When Cathe does the "one leg on the ball" moves, you could put one foot on the floor to add stability.
3)Experiment with different arm positions. If you put your arms on the floor out to right angles with your body, you will be more stable than if you keep them close to your sides.