Personally, it depends on how your fitness level is. But, if you are new to Cathe, I would tell someone but the Step with at least two risers. You are going to need two risers because of the exercises. I would buy a good mat. I would buy one with good cushion. I wouldn't buy a mat that is thin because it will hurt your knees. Also, I would buy weights, 1 pound, 2 pounds, 3 pounds, 5 pounds, and 8 pounds. I would buy the weights that aren't metal, but feel like rubber. Also, you can buy loops and stretchy bands. As for a barbell for squats, you can, but if you are a beginner, you probably are not going to focus on it. But, you can use your weights for that, right now. Eventually, you will get stronger and you will want to invest in a barbell. A high step, I got mine later because Cathe has a lot of workouts and the high step isn't is a lot of them.
As for a barre, I would suggest find a good chair that is up to the middle of your waist. But, when you are really into the workout like 6 months, then think about investing in her fit tower. I bought her fit tower this month and waiting for it. Also, you can use a wall for some of the barre exercises.
As for the bike, that is your preference. I don't use a bike because I don't like bikes. I think it isn't necessary. Cathe has so many other workouts, you can get a good workout without it. If you love bike, then do it. I don't like it. I don't like the seat.
It depends if you like Cathe workouts. You may find you don't like it. But, I do suggest investing in the dumbbells and a good mat. Any workout you are going to need that!
I hope that has helped. It is investment, but think of this! You are investing in your self! You are worth it! I have my equipment for more then a year! It lasts!