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The good old stand-by of any gym or weight training program, is used to develop strength and balance.  Dumbbells come in a variety of styles which is more a personal preference.  The more important aspect is to pick a weight you are comfortable with but also is sufficient enough to stress the muscle a a level to induce strength building.  The last reps of any exercise should tax the muscle to near failure while maintain good form.  The two go together.

The name “BOSU” is an acronym for “Both Sides Up” or "Both Sides Utilized", meaning the trainer could be used on either side, the dome or the platform.  Similarly to the physio ball, the BOSU trainer is used to induced instability and thus force your body to constantly adjust its balance, leading to greater degree of muscle activation.  Studies demonstrate that performing exercises on an unstable surfaces activates the core muscle to a greater degree.  In addition, numerous studies recommend that athletes that perform on an unstable surface - read skiing - should train on an equally unstable surface.

The heavy duty inflatable ball is known by many names including, physio ball, fitness ball, Swiss ball, exercise ball and balance ball.  Originally developed for physical therapy sessions, the ball is now standard equipment in most gyms.  Because of the induced instability, it constantly requires the body to adjust balance, which forces engagement of many more muscles, and is particularly effective at promoting core-stabilization and core-strengthening.

More recently known as a "medicine ball" - the use of a weighted "ball like" training aid dates back to ancient Greece.  It is effective act activating the kinetic chain and is used in CoreSkiing to build balance and strength, particularly in the muscles of the torso.

The kettlebell originated in Russia as a counter-weight used by farmers to weigh their crops.  Now days it has found its way into most gyms as well as the CoreSkiing program.  It is particularly effective at activating the kinetic chain due to the leverage and instability it induces in the body.

The weighted bar is used in association with the BOSU ball to build strength and balance.

The term "plyo" originates from the term "plyometrics" which is in reference to "jump training".  Often its used to train for "explosive" power - where the athlete performs a standing jump to the top of the box and back down again.  The upward jump activates the concentric muscles while the drop back to ground activates the eccentric muscles.  As part of the Coreskiing program, it is used for its elevation drop for training upper thigh strength and balancene - particularly for isometric activation of these muscles - and in the Expert Level Module as well for explosive training.  However, caution is recommended due to the potential for injury, particularly knee inflammation associated with the drop.

The Power Rack is likely to be your biggest single investment in a home gym but next to a barbell set is considered to be the most important piece of equipment in the room.  All the primary strength training exercises from bench press, power cleans squats can be performed with a power rack.  On top of that, a correctly designed and outfitted rack can prevent serious injury with the use of safety stops.  There are a number of suppliers of racks available these days but one that I have personal experience with and highly recommend are racks provided by Rogue Fitness.

Barbell plates come in all sizes and materials.  From solid metal, "bumper-plates" which are mixed rubber/metal, to combination of vinyl/plastic filled with concrete.  Depending how you intend to use the barbells, you can get by on in-expensive all metal plates or move to higher cost bumper plates.  The bumper plates are particularly useful for olympic lifts as well as deadlifts since they can absorb the shock of being dropped on the flooring.  Plates come in lb or kg and typically range form 10lb, 25lb, 35lb and 45lb weights. Metal plates usually vary in diameter across the weights while bumper plates also have a consistent diameter between the various weights which is helpful in distributing load when impacting the flooring.

Starting Strength has been called the best and most useful of fitness books. The second edition, Starting Strength: Basic Barbell Training, sold over 80,000 copies in a competitive global market for fitness education. Along with Practical Programming for Strength Training 2nd Edition, they form a simple, logical, and practical approach to strength training. Now, after six more years of testing and adjustment with thousands of athletes in seminars all over the country, the updated third edition expands and improves on the previous teaching methods and biomechanical analysis. No other book on barbell training ever written provides the detailed instruction on every aspect of the basic barbell exercises found in SS:BBT3.

There is a difference between Exercise and Training. Exercise is physical activity for its own sake, a workout done for the effect it produces today, during the workout or right after you're through. Training is physical activity done with a longer-term goal in mind, the constituent workouts of which are specifically designed to produce that goal. Training is how athletes prepare to win, and how all motivated people approach physical preparation.

Practical Programming for Strength Training 3rd Edition addresses the topic of Training. It details the mechanics of the process, from the basic physiology of adaptation to the specific programs that apply these principles to novice, intermediate, and advanced lifters.....