A ballast ball is a stability ball with 2.5 pounds of sand in it made by Bosu. You will use it to perform 4 of the exercises: Ballast Ball Sides, Ballast Ball Ups, Ballast Ball Chops, and Ballast Ball Pushes. I use the 45cm size and blow it up as big as I can. The 65cm ball is a bigger than most people will want for this purpose. Power Systems doesn't carry the 45cm size, but it is available from several online sources.
A slam ball is a weighted medicine ball that doesn't bounce (or at least doesn't bounce much). You will use it, of course, for Ball Slams. A 10 pound ball is good for most people. I wouldn't go higher than 15. Get yours below.
You will use a kettle bell for the Kettle Bell Swing. The weight you use, obviously, depends on your size and strength. If you aren't sure, I would recommend a 20 pounder for a fit adult woman and a 40 for a man. Get yours below.
Battle ropes come in 1.5" and 2" diameters and lengths of 30 - 50 feet. Mine is 2" thick and 30 feet long. There is a link below to buy one from Power Systems, or you could head to your local home improvement store.
A plyo box of some sort is needed for our one jump exercise (either Down / Ups or Up / Downs). The height of the platform doesn't matter too much. You just need to be able to comfortably jump onto it from the floor several times. You will find a link to an actual plyo box below, but I have used an aerobics step and a tire for this purpose.
I do the Power Stations Workout™ - and basically live my life - in the Prio from Xero Shoes. Wide toe boxes let your toes spread and relax. "Zero-drop" non-elevated heel for proper posture. Flexible soles let your foot bend and flex naturally. Low-to-the-ground design for balance and agility.