Hi
I have the pilates performer from QVC and I really like it. It does build your core muscles and the difference between a mat or a tape is that it keeps your spine in line to work those muscles. You may hurt yourself without the track. I like it first thing in the morning for 20 minutes to get my muscles awake and going.
I have taken pilates in a gym and not being very flexable and older I actually got hurt trying to do it just on the mat. I do like the ball and that really helps the tummy area.
It would be great to have an instructor all to yourself but where I live there is no such animal and I am not sure I could afford it.