I doubt the ferret sized exercise ball is really necessary, got 1 for my ferrets and they don't even know how to roll around whilst in it. If you do decide to get one anyway, keep it away from stairs.
Ferrets can get along well and even play with other animals. Hold on to him when you introduce him to the other animals and keep an eye on how they react. If the dog has no problems around the cats, then it shouldn't be any different with the ferret.
The cage doesn't need to be very big, as long as its tall enough so that he can stand up comfortably, has enough room for a litter box, food bowl, water bottle, a blanket/old cloth for bedding, it's good. For exercise, let him out for at least 2 hours a day (1 hour in the morning before you go to work, and 1 hour at night). The rest of the time he'll be eating or sleeping (which is why ferrets are so hyper.)
Before letting him out to play, you might want to close off the places where you don't want him to wander into (close doors, block the little space that leads behind the refrigerator, patch the hole under the sofa XD .) Keep an eye on him at all times, if he feels bored he might start looking for things to climb, steal, and/or destroy. If he starts chewing on things that you don't want him to, you can get some bitter stuff (don't remember what it's called.) It can be used on furniture, wires, and hands.
For food, ferrets require a high protein diet. I give mine a 50/50 mix of 8 in 1 Ultimate chicken+rice formula and Science Diet kitten formula. Marshal is also a good brand. You don't have to do a mix, I just like to give some variety. With the Furtone supplement (comes in a bottle, there's a 8 in 1 brand and a Marshal brand with similar names, either of the 2 works), they suggest 3/4 teaspoon added daily to their food. That's a bit if an overdose, 3-5 drops daily is enough. Keeps a healthy coat and reduces shedding is all it does (he'll still shed mind you, just no tumbleweeds... eerr.. tumblehairs.) You can also give him fresh fruits as treats.
Litter training outside the cage can be a bit frustrating at times. As a ferret will mark its territories here and there, most of the time they will go in one particular area. What you can do is put a litterbox there. Any time you see him walking backwards with his tail raised if not in the litterbox, just pick him up and put him in the litterbox. You might have to do this multiple times but he'll get the idea.
Oh and keep him away from rocking chairs and tight tubes that he might try to go through.