Sharpshooter:

Knife
Sharps Rifle (20 rounds of ammo)

Infantry:

Bayonet
Springfield Model 1861 rifle (40 rounds)

Cavalry:

Saber
Colt Model 1860 revolver (2 cylinders of 6 rounds each)
Sharps Carbine (40 rounds)

Marine (Fort Fisher map only, in place of cavalry):

Bayonet
Springfield Model 1861 rifle (40 rounds)

Pioneer:

Knife
Springfield Model 1855 rifle (40 rounds)

Sapper:

Knife
Enfield Model 1853 rifle (40 rounds)
Ketchum grenade (2 grenades)

Sharpshooter:

Bowie Knife
Whitworth Patent Rifle (20 rounds of ammo)

Infantry:

Bayonet
Enfield Model 1853 rifle (40 rounds)

Cavalry:

Saber
J.H. Dance revolver (2 cylinders of 6 rounds each)
Tarpley Carbine (40 rounds)

Alternate Cavalry (some maps):

Saber
Colt Model 1860 revolver (2 cylinders of 6 rounds each)
Shotgun (double barreled)

Marine (Fort Fisher map only, in place of cavalry):

Bayonet
Wilson Naval Rifle (40 rounds)

Pioneer:

Bowie Knife
Model 1842 pistol (12 rounds)
Springfield Model 1841 "Mississippi" Rifle (40 rounds)

Sapper:

Bowie Knife
Fayetteville Armory Rifle (40 rounds)
Hand Grenades (2 grenades)

Alternate Sapper (some maps):

Bowie Knife
Fayetteville Armory Rifle (40 rounds)
Landmine (remote detonated, 1 mine)