I served in the Army in the 70s (and with the Marines in AIT school) as a Small Arms Repairman (MOS 45B20) and also served as assistant and unit armorer in my duty companies.
Items of equipment change, in this case weapons, but the SOP rarely does or does so slowly.
First off, understand that the is a double standard. There is an official set of rules and then there is the flexibility allowed by unit commanders in combat.
Who gets what firearm is determined by the unit TO&E (table of organization and equipment) and in garrison (stateside, peacetime, etc) there is damn little deviation allowed.
IF the TO&E says 2nd Plt ldr gets a rifle, he gets a rifle, even if he wants a pistol. If it says assistant MG gunner gets a pistol, they get a pistol, which ever one is the current issue standard. When I was in, the pistol was the 1911A1, today its a 9mm. Doesn't change the TO&E (just what name is in the equipment block)
Personal (and privately owned) handguns are strictly
verboten. This is the standard rule and the one rule most often ignored by COs on the sharp end. Smart commanders allow troops in "indian country" a fair amount of latitude that is not allowed outside of combat areas.
SOP for carry (all weapons) outside of actual combat ops was always chamber EMPTY. IF you were caught whith a round in the chamber, you were in for all kinds of crap, possibly up to an Article 15.
Again, this is in "secure" areas, and could be different at forward firebases, at the CO's direction.
Forget what "Wardaddy" had in a movie, tis a BS movie, not a factual documentary.
Be aware that despite the official rules there are a lot of things that happen and the brass just looks the other way, if they see them at all.
I knew a senior SSG who carried his own, personal, private, civilian Colt Govt Model. No one ever said a word to him about it. I spotted it because I got a glimpse of the gold Colt medallion on the grip. went and checked, and sure enough the M16A1 that he was supposed to have was still sitting in the arms room rack. Fortunately, I was, at the time, experienced enough to keep my mouth shut. Had I made an issue of it, I'm sure he would have gotten a little crap, but I KNOW i would have caught buckets of it, ...unofficially..
Hopes this helps you get a handle on things. There are the official rules, and there is what troops get away with, and they can be quite different, depending on the local commanders and their attitudes.