Which one do you like better? Both are made to serve a purpose, and that is to give you an aerobic workout. Some people may like treadmills better, and others ellipticals. I recommend you go with the one you will see yourself using more often.
Personally, I like the treadmill better. I always feel like I am shuffling when on an elliptical, and I also feel it is harder to get a really intense workout in on them. Again, these are my opinions. If you have the opportunity to, work out on each of them multiple times and then make a decision.
As far as using an exercise ball, there are numerous workouts you can do. Way too many to list or explain. If you have specifics I can help you out there.
Congrats on the upcoming wedding (or so it seems from your signature).