In terms of muzzle flash, noise, penetration, controlability, cost (to practice), capacity, hearing loss (or earache), and all the other variables?
There's no one that's best at everything
Muzzle Flash- depends on the loading and barrel length, I'd rate standard pressure 9mm and standard pressure .45 ACP out of full sized guns as equal in having the least muzzle flash of the cartridges mentioned. .357 Sig and .357 Magnum will be the brightest with .40 S&W somewhere in between
Noise- This one would have to go to the .45 ACP due to it's lower velocity but mild 9mm like 115grn Winchester Silvertips are particularly loud either. Again the loudest are the .357's with .40 being somewhere in the middle.
Penetration- .357 Magnum in full power loadings penetrates the most by far with the others being roughly equal.
Controlability- from lightest recoiling to heaviest in most guns 9mm, .357 Sig, .40 S&W, .45 ACP, .357 Magnum
Cost- from least expensive to most expensive 9mm, .40 S&W, .357 Sig, .45 ACP, .357 Magnum
Capacity- 9mm will typically have the highest capacity, .40 and .357 Sig will be the same, .45 will be the lowest in an auto, and .357 Magnum will be limited to 5-8 shots because it's a revolver round.
Hearing loss- is basically the same as the noise criteria
Other variables- the first question is do you prefer a revolver or semi-automatic. If you like the revolver, then the .357 Magnum is the most logical choice. Another factor is versatility, the .357 Magnum is the most versatile cartridges as you can use everything from mild .38 Special loads to heavy hunting loads in the same gun, .45 ACP would be next in line for versatility with the other three being tied for third place. Do you or will you reload? If you do or might, the .357 Magnum makes a lot of sense as you can use lead bullets for inexpensive practice and being a revolver you don't have to chase down your brass. Affordability and quality of carry ammo is another thought, .357 Magnum and .45ACP are still pretty good with older, more economical carry ammo such as Winchester Silvertips and Remington Semi-Jacketed hollowpoints while 9mm really needs more modern premium bullets like Winchester SXT, Speer Gold Dot, or Federal HST. .40 and .357 Sig are newer cartridges and thusly the majority of ammo available for them has newer premium bullets.