The following weapons were used in the OVA Bubblegum Crisis:
Beretta 80 Series Pistols - "Cheetah"
The Beretta 80 Series Pistols - "Cheetah" is a go-to pistol in the series, being used by Quincy's guards, and in a Vision music video.
In "Revenge Road" (E04), Gibson uses a Bren Ten to shoot at his wall.
In "Moonlight Rambler" (E05), Sylvie uses a Colt M1911A1 when infiltrating "The Tower".
In "Moonlight Rambler" (E05), Kaufman attempts to defend himself with a CZ 75 "First Model", which is a favorite of the series' character designer, Kenichi Sonoda.
In "Tinsel City" (E01), Priss uses a weapon designated "Member II". Essentially, it is an emergency weapon, a takedown rifle-style pistol most closely resembling the AR-15-pattern FightLite Raider pistol (developed decades after the cancellation of the series). It seems to have a 3-round magazine, possibly in a caliber greater than the expected 5.56mm.
Unknown Semi-Auto Pistol
In "Double Vision" (E06), Nene is seen at the AD Police shooting range utilizing an unnamed fictional pistol to engage in hoplotherapy. It most closely resembles the Colt SCAMP.
The Ruger Redhawk appears to be Leon's AD Police-issued sidearm.
In "Double Vision"(E06), Leon is seen using a fictional large-caliber revolver, with a capacity of 3 rounds. This is designated (according to markings in the spinoff "Bubblegum Crash") the ERTH-SHKR, likely created to deal with the increasing armor capabilities of new "Boomer" models.
Unidentified Smith & Wesson Revolver
A guard at the police station uses what appears to be a Smith & Wesson revolver on guard duty, judging by the (reversed) cylinder release latch. It features a shrouded hammer.
In "Revenge Road" (E04), police officers utilize unidentifiable revolvers in an attempt to subdue Gibson.
The AD Police standard primary weapon appears to be a fictional automatic carbine by the name of "C-69" (according to official artwork). It is obviously heavily inspired by the "M41A Pulse Rifle" from the film "Aliens". However, instead of being purely Thompson-based, there seem to be elements of the Walther MPL, as well as a fictional pump-charging mechanism.
In "Revenge Road" (E04), regular police officers are seen using Ingram MAC-10s in an attempt to subdue Gibson.
In "Revenge Road" (E04), the Knight Sabers train with IMI Uzis seemingly loaded with simunitions.
Unnamed Fictional Submachine Gun
Unnamed Fictional Assault Rifle
In "Moonlight Rambler" (E05), Meg utilizes a fictional assault rifle, seemingly based off of the AR-15 in some capacity, in an attempt to hold off "Doberman" Boomers. It appears to use the water jacket of a Vickers Machine Gun as a handguard, with the barrel flush with the jacket's front.
Unnamed Fictional Bullpup Assault Rifle
In the same standoff, Lou uses a fictional bullpup assault rifle, most closely resembling a Bushmaster Arm Pistol.
In "Double Vision"(E06), Reika Chang is seen utilizing a shotgun most closely resembling an Ithaca 37 in a music video.
Unnamed Fictional Shotgun
The AD Police, as well as GENOM security guards, utilize unnamed fictional pump action shotguns. They most closely resemble Mossberg 500 Cruisers, judging by the ejection port.
Priss's secondary hardsuit (formed by combining her standard hardsuit with her motorcycle) utilizes a machinegun most resembling the MG42, with a carrying handle seemingly stolen from the M41A "Pulse Rifle" from Aliens.
General Dynamics M197 Vulcan
A common heavy weapon, mounted on both AD Police Personal Helicopters and Boomers alike, is the General Dynamics M197 Vulcan.
Unknown Fictional Grenade Launcher
In "Tinsel City" (E01), Leon utilizes what appears to be a grenade launcher resembling Priss's "Member II", but utilizing a break-action loading system and upscaled to 40mm or so.