(My answer is going to be heavier on the police side.) Pistols would have be largely revolvers with a few areas semi-automatic pistols (nearly always using 1911 models), this would remain the case until the mid 80’s when the “semi auto revolution” occurred. Some of the most common pistols were:

Colt double-action revolvers firing .357 Magnum such as the Python, Trooper.

Smith & Wesson Model 15, Smith & Wesson Model 36

Colt .38 Special revolvers such as the Cobra, Agent, Detective Special models.

A few carried the famed Smith & Wesson Model 29 chambered in .44 Magnum (the Dirty Harry gun) were used but not as common due to the size and the strength of the round.

With the rise of police tactical teams that had started in the US during the 60’s and expanded rapidly through the 70’s as SWAT teams became common place in large departments, new weapons began to appear in police armories that had previously been dominated by WWII surplus (M1 Garand, M1 carbines, Thompsons). The M16s and AR-15s (along with a few other .223 rifles such as the Ruger Mini-14) began to be incorporated in these units.

With the rise of SWAT teams came police snipers, thus sniper rifles (which like the US military have largely used variants of bolt action hunting rifles until the past decade or so). The Winchester Model 70 was used by LAPD SWAT snipers early in the formation but like the US military a great deal SWAT snipers switched to Remington Model 700. There was also limited use of the M14/M1A used as both sniper and battle rifles.

While there was dozens of various shotgun used by various LEOs during the time frame the Mossberg 500 ,and Remington 870, and Ithaca 37 are some of the noticeable selections as both Mossberg 500 and Remington 870 still remain two of the most popular shotguns to this day (in civilian, military, and law enforcement).

Can I assume that you are asking about US police and civilians?