Shamelessly ripped from the DoD Manual:

Allied Classes Rifleman Primary Weapon: M1 Garand or M1 Carbine Primary Ammo Loadout:11 clips, 8 rounds each Secondary Weapons: Colt Pistol, Knife Grenades: 2 The Rifleman - aka "Light Infantry" is a good all around class - deadly at both long and short range. Not as effective on the move or in assaults, however. Sargeant Primary Weapon: M1 Thompson or Grease Gun Primary Ammo Loadout (Thomspon): 7 clips, 30 rounds each Primary Ammo Loadout (Carbine): 11 clips, 15 rounds each Secondary Weapons: Colt Pistol, Knife Grenades: 1 The Sargeant is a class designed for assaults, as well as close-in engagements. With the Thompson, he can "spray and pray", while with the Carbine he needs to pick his shots more carefully. Support Infantry Primary Weapon: Browning Automatic Rifle (BAR) Primary Ammo Loadout:12 clips, 20 rounds each Secondary Weapons: Colt Pistol, Knife Grenades: 1 The Support Infantry is a hybrid of the Rifleman and Sargeant classes. His BAR packs enough firepower and accuracy to be deadly at almost any range, although his clip capacity and slower speed limit him on assaults. Sniper Primary Weapon: Springfield Sniper Rifle Primary Ammo Loadout:11 clips, 5 rounds each Secondary Weapons: Colt Pistol, Knife Grenades: None The Sniper is a tricky class to play. Although he requires team support on the move, once he's found a good position, he can hold his own against entire squads of enemies.  Machine Gunner Primary Weapon: .30 Caliber Machine Gun Primary Ammo Loadout:2 boxes, 150 rounds each Secondary Weapons: None Grenades: None Like the Sniper, the Machine Gunner requires the support of teammates to be effective. On the move, his undeployed weapon is virtually useless, and with no secondary weapons, he is very vulnerable. Once in position, a good Machine Gunner can decimate anything unfortunate enough to be in it's path. Once a Machine Gunner runs low on ammo, however, he will need a teammate to pass ammo boxes - since once again he has no secondary weapon. Airborne Primary Weapon(s): All Primary Ammo Loadout(s): All Secondary Weapon(s): All Secondary Ammo Loadout(s): All Grenades:All Airborne troops will only appear on "Para” maps. Paratroopers can select from any normal weapon, as well as paratrooper-specific weapons. (The Greasegun and folding stock Carbine) Like normal classes, they carry a number of grenades depending upon the primary weapon that they choose.

Axis Classes Grenadier Primary Weapon: Karbiner 98k Rifle with Bayonette or Karbiner 43 Primary Ammo Loadout:13 clips, 5 rounds each Secondary Weapons: Luger Pistol, Spade Grenades: 2 Like the Allied Rifleman, the Grenadier is a very versatile class. In addition to his accurate, powerful rifle and attached bayonette, he also has two grenades with which to cause havoc. Unteroffizier Primary Weapon: MP40 Machine Pistol Primary Ammo Loadout:7 clips, 31 rounds each Secondary Weapons: Luger Pistol, Spade Grenades: 1 Like the Allied Sargeant, the Unteroffizier is a class designed for assaults, as well as close-in engagements. This class is very similar to the Scharführer class, although the MP40 trades damage for reduced recoil. Scharführer Primary Weapon: MP44 Assault Rifle Primary Ammo Loadout:7 clips, 30 rounds each Secondary Weapons: Luger Pistol, Spade Grenades: 1 The Scharführer has no real allied counterpart. His primary weapon, the MP44 - was the first true "Assault Rifle" - the only one in WW2. It struck a great balance between stopping power, range, clip capacity, and recoil that was unmatched by most weapons.  Scharfschuetze Primary Weapon: Karbiner 98k Sniper Rifle Primary Ammo Loadout:13 clips, 5 rounds each Secondary Weapons: Luger Pistol, SS Knife Grenades: None The Scharfschuetze is a tricky class to play. Although he requires team support on the move, once he's found a good position, he can hold his own against entire squads of enemies. MG-Schütze Primary Weapons: MG42 Machine Gun, or MG34 Machine Gun Primary Ammo Loadout (MG42): 2 boxes, 250 rounds each Primary Ammo Loadout (MG34): 5 cans, 75 rounds each Secondary Weapons: None Grenades: None The Machine Gunner was the backbone of German Military doctrine, and in turn the MG-Schütze is very important to any squad. Like it's allied counterpart, the MG-Schütze requires support on the move, and extra ammunition once it's deployed. Allthough the MG42 provides more raw firepower, the MG34 trades clip capacity and rate of fire for accuracy and lighter recoil. Fallschirmjager Primary Weapon(s): All Primary Ammo Loadout(s): All Secondary Weapon(s): All Secondary Ammo Loadout(s): All Grenades: All Fallschirmjager troops will only appear on "Para” maps. Paratroopers can select from any normal weapon, as well as paratrooper-specific weapons. (The FG42 and K43) Like normal classes, they carry a number of grenades depending upon the primary weapon that they choose.