You will achieve best results with the ball, but I wouldn't waste money on the core secrets stuff. I have both DVDs (pilates and core secrets).
If you buy yourself a fit ball you can do your upper and lower body workout incorporating the ball....which automatically works your core.
Pilates is all about "breathing" through your core muscles....basically we all breath wrong. Our stomach should go out as we inhale and suck in (draw your abdo towards your spine) as you exhale. That's the secret of Pilates, and yoga, and fit ball...blah, blah, blah! Personally, I found Pilates extremely hard on my lower back....and I don't generally have a back problem!!
I have had great results with a fit ball workout.
If you wanna know anymore just PM me and I'll give you some more specifics....free of charge!!