Glad you are carrying a "game changer" in other words a weapon that will quickly render the gunfight over with you as the victor.
That said, there is a great deal of debate as to what that really means. The .45 has a great deal of stats to recommend it; with hollowpoint, high velocity ammo making it even better.
The 10mm has a lot going for it, with 135 gr ammo from Double Tap acting at 41 Magnum levels or the 175 grain Silvertip by Winchester.
The 357 Sig is hot, with a 125 grain bullet at a good 1400 fps in a good gun (try to get a 5 inch barrel).
In revolvers, the 357 Magnum (and by extension the 357 Sig) is THE top man stopping round in 125 grain soft hollowpoints. The 41 Magnum or 44 Magnum are there as well but too powerful for a beginner but with the 44 you can shoot 44 Special or reload low powered 44 mag practice loads forever.
Any of these selections is what might be considered a major stopper.
Second tier calibers are 9mm+P, 40 S&W, 44 Special, etc are fine rounds, but do not have the energy/velocity numbers you are seeking.
The argument for which is better is loud and complex. My recommendation is buy what you can get a lot of ammo to shoot say 1000 rounds a year. This can be hardball or you have to commit to reloading, or just a lot of money but just make sure you are getting in the practice.
Good Luck and Welcome.