Welcome to TFF, rogue! Glad to have you with us.
The 1960s were really a time of change in terms of military firearms, most especially for the U.S.
In the 1960s, the standard military issue pistol for the Soviets was the The Makarov PM 9x18 caliber (Pistolet Makarova) though the older TT-30 (7.62 mm Samozarjadnyj Pistolet Tokareva obrazca 1933 goda) was still in use to some extent as well. The Makarov remained in use until 2003 when it was replaced by the Yarygin PYa. As for machine guns, the Soviets relied on the RPK light machine gun primarily.
In the 1960s the U.S. switched from the M-14 (7.62 NATO) to the M-16 in 5.56 NATO caliber for its general issue rifle. As for handguns, the U.S. still issued the venerable 1911 Colt in .45 ACP caliber. Other NATO nations, however, used various pistols in 9mm para bellum caliber. As for machine guns, the most commonly used by the U.S. was the M-60 (7.62x51) and, of course, the venerable M-2 .50 caliber machine gun.