The standard-issue sidearm for GUN soldiers in the game is the Heckler & Koch USP Tactical. When Shadow is confronted by the GUN Commander in a cutscene, the Commander attempts to shoot Shadow with his USP Tactical, but misses. The gun has a 10-round capacity in-game, and fires semi-automatically.
M1911A1
In some pre-rendered cutscenes, GUN soldiers use M1911A1 pistols. A silhouette of an M1911A1 also appears on GUN supply crates. Shadow is seen holding an M1911A1 in promotional images and the opening sequence, but he never uses one in game. It's possible that at some point the M1911A1 would have been the standard pistol and was changed
to a USP Tactical.
Desert Eagle
The "Shadow Rifle" appears to take some elements from a Desert Eagle, although it's not clear what model it was inspired by.
Submachine Guns
Heckler & Koch MP5A3
GUN soldiers also use the Heckler & Koch MP5A3 with the Navy trigger group. The gun is fully automatic with a 20-round capacity while used by Shadow. The opening title sequence of the game shows Shadow a much more detailed and accurate MP5; in this cutscene, Shadow rather infamously cocks the weapon by pumping its handguard like a pump-action shotgun, with the handguard even visibly moving during the animation.
Rifles / Carbines
SIG SG 551
The standard assault rifle used by GUN soldiers is the SIG SG 551. When picked up by Shadow, it has a 30-round capacity.
Walther WA 2000
The "Laser Rifle" appears to be inspired by a Walther WA 2000. It holds 20 shots.
Machine Guns
Browning M1919
A heavy machine gun that appears to be loosely based on a Browning M1919 appears in the game. It is mounted on turrets which can be used as a stationary weapon (with unlimited ammo) or destroyed and used as a handheld weapon with a 30 round box magazine (somehow a stock and pistol grip appear on the gun when it is destroyed). The weapon also appears in the hands of GUN combat robots and in crates later on in the game. Oddly, it can be fired faster in semi-auto than in full-auto.
GE M134 Minigun
Handheld GE M134 Miniguns can are dropped from GUN's F-6 "Big Foot" Walkers (despite the fact that, like in Sonic Adventure 2, the "Big Foot" walkers are depicted with fictional 3-barreled miniguns). As expected, they are massive in comparison to Shadow and are held by a strange pistol grip. They are arguably the game's best weapons due to their 40-round magazines, high damage, and fast rate of fire, but they are somewhat usurped by their relative sparsity.
Launchers
Milkor MGL
GUN soldiers also use the Milkor MGL grenade launcher with the stock and Armson OEG reflex sight removed. It holds six grenades.
M136 AT4
GUN soldiers also use the M136 AT4 rocket launcher. It holds six rockets.
The "4-Shot RPG" and the "8-shot RPG" appear to be loosely inspired by an M202 FLASH.
Unused
Colt Gold Cup National Match
An unused weapon icon that depicts a Colt Gold Cup National Match can be found in the games files. It is identified mainly by the slanted slide serrations and the grips. It can be seen in early screenshots.