Welcome Bev! I just love to give other people the info. they need to shop. I'm such an enabler!
Anyway, when buying a stability ball the first thing you need to determine is what size you need. If you are 5'2" or less, then 55 cm is the correct size, 5'3" to 6'0", then 65 cm, and 75 cm for heights above that (I'm not 100% sure about the heights so check what is says on the ball you pick up). As for a particular brand, I don't think it matters hugely although make sure to get a burst resistant ball.
For a barbell you can do one of two things. Both Wal Mart and Target have sets where the bar weighs 5# and then they come with a variety of plates. I think the Wal Mart set is by US something or another and the Target set is their own store brand of fitness equipment. The second option is via the internet. If you would like to have the set that Cathe uses in the Intensity and Body Blast series, it is the Troy Lite system and is available at wwww.fitness1st.com.
As for the step, you will want to purchase the original step and it should be available in either the traditional teal top with purple or pink risers or the gray top with black risers (or is it vice versa). The home step is smaller and is not as good to use for strength exercises as the full size model.
BTW, all the equipment mentioned should be available at the website listed above (you may want to consider this option because it will just come to you vs. you having to go to different places to gather it all yourself).
And don't forget that depending on the videos you have you may want to consider some other equipment (if you don't have it already). You may need to get several sets of hex dumbbells in varying weight (actually, this are pretty much a necessity for most of Cathe's strength workouts). You may also want to consider a high step (the high step is available in some retail sporting good stores or at
www.fwonline.com), a medicine ball, and a body bar down the line. These are definitely not required but if you get into Cathe, will be welcome additions later on.
HTH,