If you have the money, some focus mits and some gloves will really help your fitness. You'll need either your brother or a friend to hold up the mits, but you can swap when you are worn out.
You must, and i repeat YOU MUST buy some hand wraps and learn how to wrap your hands. You are likely to injure your wrist if you don't use hand wraps.
Try to incorporate punching combos in by adding punches as you go i.e 1) jab 2) jab, jab 3) jab, jab, straight 4) jab, jab, straight, duck 5) jab, jab, straight, duck, left hook. 4) jab, jab, straight, duck, left hook, right uppercut.
Speedball is great for the shoulders, floor-ceiling is great for reflexes and hand-eye coordination, heavybag is great for building power and for conditioning. The mitts are good if you have someone to knows how to do it properly. But basically everything in boxing uses bodyweight, there are no weights (if there are any, they're very light weights, usually used for shadowboxing to increase speed). Loads of pushups, situps, chinups, pull-ups, squats, burpees... all of that sort of stuff.
Sparring is a good exercise, but it's very boxing-specific, designed to work on technique and refine skills, rather than for conditioning. Still, it's a very hard workout. Just don't try to be a hero, use headgear and at least 12oz gloves (preferably 14 or 16oz).