My son is a pilot with NWA. When the armed pilot program first began the pilots furnished their own guns at their expense, and AFAIK they still do. IIRC the only approved pistol at the time was the HK USP and only in 9mm, but that may have been changed by now to include the .40 and .45 caliber HKs. I know that if it was my choice I would choose the .45 which I am very familiar with. The .45 caliber round that is, not the HK pistol. I'm sure it's a fine piece of work, but I have been using Colt 1911s for many years now and I don't see any reason to change horses in midstream.
My son chose not to buy another expensive gun and take the mandatory training class at the FBI range in VA at his own expense, so he doesn't carry a gun on board although he often flies with captains who do.