What home gym equipment do you need?
Nothing...Really, you don't NEED anything. The ground and gravity are the perfect workout tools giving us running, air squats, press ups, planks, yoga and burpees. Any half decent trainer could work you to exhaustion and help you build a killer body using nothing but your own bodyweight and a bunch of exercises any school boy would know.
That being said, having a range of tools is more fun and will get you to your goals much faster.
In my opinion, a serious home gym owner needs the following:
1) Yoga or exercise mat. Obviously great for stretching but also useful for ground based exercises like sit ups, planks, turkish getups etc.
2) Suspension trainer. I use one everyday for stretching and at the end of most workouts for core work. I love them for isolating muscles and working biceps and triceps and are one of the best ways to do lunges.
3) An olympic barbell and plenty of weights. The best tool for building strength. Deadlifts, squats and presses are the cornerstone of any strength training program and pretty much all you really need to do.
4) Squat rack or power rack and a bench. If you have the space this is pretty essential if you have an olympic bar and want to do strength training.
5) Some dumbells and/or kettle bells. A random assortment is fine. Buy some when they're on sale or at a garage sale and add to your collection as you go along and figure out what where the gaps are but every weight is useful, even the very lightest ones.
6) Gym flooring.
7) Chin up bar. You might not need one if you have a power cage but they work best if you can hang fully extended with your feet off the ground.
8) Skipping Rope. So cheap, so compact and so effective.
Notable Mentions: Booty bands, swiss ball, yoga blocks, cable pulley system, plyo box, weight belt and some kind of cardio machine like treadmill, rowing machine etc.