Going with the later 1940's, here's pretty much what you'd see in an Oklahoma lawman's armory.
Remember, these were civilian cops, and didn't have a lot of money.
You'd very rarely see any kind of even remotely exotic firearms in their hands, and unless it was a bigger department you usually wouldn't see much in full-auto weapons.
Pistols:
In an automatic it would have been a Colt 1911-A1, most likely a commercial, but possibly a military surplus.
The only other autos around would have been surplus 9mm's and no one would have been carrying one of those.
For something different he could have owned an early Colt aluminum .45 Commander introduced in 1949.
It's possible he could have a Colt Super .38 as it was then known, but the Super .38 was a very rare gun in those days.
Revolvers:
S&W DA revolver, either a large "N" type frame in .44 Special or .45 Colt, possibly a .357 Magnum.
In .38 Special, the S&W Model 10.
Colt would be an Official Police .38 Special, possibly a New Service in .357 or most likely 45 Colt, possibly a surplus Model 1917 in .45ACP.
Out there, a Colt Police Positive Special wouldn't be too common.
If he had a "snub nose" .38 Special it would have been a Colt Detective Special, nothing else.
Shotguns:
Prime law enforcement guns were the Winchester Model 1897 or Model 12. Winchester pretty much owned the police market.
For other brands, the Ithaca Model 37 was around.
In semi-auto shotguns the Remington Model 11/Browning A5 were the only automatic shotguns trusted or even readily available and western cops did like them.
You might find a few other brands of shotguns but these weren't common. You had to look to find someone with anything but a Winchester pump gun.
Rifles:
The standard Winchester Model 1892 or the Model 1894 were popular, you might still see a Winchester 30-06 Model 1895.
A surprising number would have US military surplus Springfield 1903's and possibly a Model 1917 American Enfield.
In commercial bolt action rifles, the Winchester Model 70 and Remington Model 30 were about it.
In semi-auto rifles the Remington Model 8 in various calibers like the .30 or .35 Remington and especially the Winchester Model 1907 in .351.
The Winchester especially was a big law enforcement rifle before WWII in the hands of the FBI and Western lawmen like Ranger Frank Hamer who like many lawmen sent his Winchester to a gunsmith in Joplin Missouri to be fitted with a 30 round magazine.
If he had a semi-auto rifle in the late 40's it would almost certainly be the Winchester.
In automatic weapons, it would be a Model 1921/28 Thompson gun, or a surplus military BAR or possibly a commercial Colt Monitor, which was a commercial sales BAR for the police.
It's unlikely you'd see a M1 or M1A1 Thompson or M3 Grease gun that early. At the time they were still standard military issue and not many were out of military control yet.