Dumbbells for strength training, they're space saving and easy to move around in your space and kettlebells are great for strength and endurance training
To increase your mobility and continue with strength training resistance bands are fabulous. They take up no space and you can take them with you when you travel as well.
If you like to incorporate aerobic workouts into your fitness routines step platforms and jump ropes offer great lower-body workouts.
Cardio machines for a home gym might include a foldable pedal machine, a treadmill or a stationary bike.
Yoga mats, and foldable benches are good essentials to add to a home gym.