There really isn't any good kit that serves all needs, so most shooters eventually just build their own kit.
Buy a fishing tackle box and label compartments for each caliber.
Buy GOOD one-piece stainless steel or carbon fiber rods and buy the tips, patches, and brushes for each caliber.
This way when you add a new caliber, all you have to do is buy tips and brushes.
Usually, for rifles and shotguns you can get by with two one-piece rods, and one pistol rod.