The hanging heavy bag is the best overall boxing tool, and I like doing a lot of open handed work on it to get limber for punching and to chain the motions necessary for optimal force transfer. It is also the place to practice survival boxing applications if you want to survive the legal end of the encounter. The hanging bag also gives you plenty of anti-clinching opportunities. The other bags are listed below in their order of importance.
Double-Ended Bag
Buy it or make it. I like switching out double-ended bags from the same station, with a light store bought air-bladder ball bouncing tightly, and a slack homemade variety giving off-speed work.
Make a double-ended bag by imbedding a short bungie cord inside of a heavy roll of Scott paper towels and then adding a pound of duct tape to make it one unit and covering it with a half pound of electrical tape. Place an eye-screw in the ceiling and hook a bungie cord from it to the top of the padded tube. For the floor anchor I like a truck strap wrapped around a stack of barbell plates. Pad the cord hooks with pipe insulation and mount at head level.
Never throw two punches from the same position against this bag. Practice moving round tracking it with your jab, hit it with a straight and then clean up with a jab.
Reflex Bag
This speed bag, mounted upside down on a free-standing truck spring, is perfect for the apartment dweller or for a karate school or other gym that has drop ceilings and can hang bags. I will do a specific article on the use of this bag.
The Speed Bag
This underrated and miss used tool is noisy for a home gym. I have done an article on its use here Speed Skull.
What is your opinion on the double double-ended bag?
I think it is essential for eye-hand, and like it for practicing defensive combinations and counter punching.
The reflex bag and speed bag allow you to get by with rhythm. the double ended bag is the only thing tat tests your speed as far as apparatus in the gym.
It was one of the first modern bag designs and languished in obscurity for 80 years or so.