Unless you have a lot of extra money, stretching machines are a waste of money. Free-stretching on the floor or placing a leg on objects of increasing height, such as steps on a stepladder, work just as well. Other low cost alternatives include sitting on the floor with the legs spread and pulling the upper body forward or toward the side by pulling on the ends of a rope wrapped around a stationery object; and using a rope and an overhead pulley to pull the ankle of a leg to higher heights. Be careful when doing this since it takes some practice to keep you balance. Obtaining flexibility does not require a machine; it requires that you perform serious stretching exercises daily, outside of martial arts
You go to Taekwondo class to learn Taekwondo. A side effect of the training is that during class you increase your strength, flexibility, endurance, etc. However, these things are best increased by training outside of class.
You could spend a lot of money to attend a fitness gym, or you could set up your own home gym in which to train. You could spend a lot of money on overpriced machines for your gym, or you could buy or make a few simple tools that will work just as well, if not better, as the expensive machines.
The speed bag has been used by boxers for ages as a way to improve their hand speed and timing. If the bag is used a lot the swivel will quickly wear so insure it is of top quality. Wood backboards may warp if left outside. Fiberglass backboards are more durable and weather resistant. If the unit is left outside, remove the bag after use and protect it. Leather bag gloves are necessary; the gloves may also be used when using the heavy bag.