The Beretta M1951. This is the lvl 3 pistol. Incorrectly called the "Delta M1911". It is found in Florida, it appears to have a silencer and it holds 8 rounds.
Colt M1911A1
The silenced nickel-plated Colt M1911A1 with hammer from anachronistic Colt XSE is the lvl 2 pistol. It is found in Florida and it holds 7 rounds.
Luger P08
The Luger P08. This weapon is called the Pistol Lv.1. This is the 1st weapon you use in the game. This weapon is used by Dominic to guide Michael, Fredo and Aldo out of Havana.
Revolver
"Magnum Enforcer .501"
Smith & Wesson Model 12
The Smith & Wesson Model 12 appears as the ".357 Magnum" in the game (Although in reality this gun fires .38 Special). It is a very powerful weapon killing people in either one or two shots. It has a black finish. Used by Aldo in Cuba to escort Michael and Fredo. When he is killed Dominic takes the gun. When you're back at New York you have it. Level 1 magnum.
Smith & Wesson Model 29
The Smith & Wesson Model 29. The lvl 2 magnum, called ".44 Magnum Force" in the game, possibly a reference to the Dirty Harry film on the same name. It is found in New York, it holds 6 rounds and it is extremely powerful.
Submachine Guns
M1928A1 Thompson
The M1928A1 Thompson is used in the game by almost everybody in the game including your family. In game it has a 50-round drum magazine, but it holds 40 rounds. It is called the Tommy Gun in game. It is the level 1 gun of its type first seen in Cuba used by the military.
MP40
The MP40. The lvl 2 Automatic, called "MP38" in the game. Used by Dominic's men if they have the right license, and by other families, but only their high ranked men. Found in Florida. It holds an incorrect 50 rounds.
Assault Rifles
AK-47
The AK-47 is the level 3 machine gun, has a 60 round drum and you can carry 300 bullets, it also appears to have some type of peephole sight in game. Found in Cuba. It is used by the hitman who drives by Dominic's house in Florida. Used by high ranked people, it requires expert gun License. It seems that his drum magazine is taken from RPD, which would be incompatible in real life.
Shotguns
Browning Auto-5
The Browning Auto-5 appears as "Schofield Semi-auto". This is the lvl 3 shotgun, it is found in Florida it holds 5 rounds, used by Dominic, his men with expert gun license and high ranked enemies like Don Granado.
Double barrel Sawn off Shotgun
The Double barrel Sawn off Shotgun. The level 2 shotgun is a Sawn off Double Barrel Shotgun of unknown make and model. It holds like it should 2 rounds. It is found in the Corleone Compound it can be obtained at the beginning, easily replacing the level 1 shotgun.
Winchester Model 1912
The pump-action shotgun, vaguely reminiscent the Winchester Model 1912 is the level 1 shotgun. This weapon is used by almost everybody in the game. The shotgun is treated as being single-shot, with the pump animation counting as a reload animation, which means player character never loads new shells into the tube magazine.
Rifles
"Spitzer Centerfire"
The fictional sniper rifle, named "Spitzer Centerfire" (that complete nonsense, because these are just two terms relating to ammo) and remotely resembling the AK-based sniper rifles such as the Galil or Zastava M76, appears as the Level 2 sniper rifle, and can be found in Florida. It holds 5 rounds.
Izhmash SV-99
The Izhmash SV-99 with suppressor appears as "SR-98", and holds a 6 rounds instead a real five. This is the Level 3 sniper rifle, and found in Cuba. It is used by Dominic, his men if they have the license, and few high ranked enemies.
This is a massive anachronism (even considering the general anachronisms of this game) - the SV-99 was not available until 1999. It's also ridiculous to portray the SV-99 as a powerful weapon, as it shoots .22 rounds, and was developed primarily for use by special police forces to particular purposes, such as the destruction of light sources. Based on it's in-game name, the developers possibly have confused it with the powerful SV-98 (a equally anachronistic).
SVD Dragunov
The SVD Dragunov appears as "MG-S1 Sniper Wolfe" and incorrectly holds 5 rounds. Level 4 sniper rifle, it could only be available by downloadable content.
Winchester Model 70
The Winchester Model 70 appears as "Sniper Carbine", and it's a Level 1 sniper rifle. This weapon is also used by a Cuban to kill Aldo Trapani in Cuba at the beginning of the game. It is also used by Dominic when he attempts to kill Fidel Castro. It don't has a reloading animation, and are treated as drawing from a single ammunition pool with a delay between shots.