Weapon List: (Locations are obviously not the only place you can find a certain weapon but if you are missing any they should help you find them. The specific locations are generally the earliest opportunity to get that weapon.)
Sub-Machine Guns
KP5 - Available from the Start.
DK7 - Unlocks automatically at the end of Mission 02.
Kurtis 45ACP - Unlocks automatically at the end of Mission 08.
PDW-46 - Mission 01, Same table as the first intel, just before going down off the bridge.
C9MM - Mission 05, after the bridge at the start when you reach the amush site there are 3 enemies. One of them should drop this.
F90 - Weapon of choice for the female enemy troops towards the end of the game. If looking for this specifically just start Mission 14 and go up the first street. There is one of those troops in the group there. These are pretty plentiful through the later stages of the game though.
Assault Rifles
ACR - Available from the Start.
IAR 556 - Unlocks automatically after Mission 01.
FAMAS G2 - Unlocks automatically at the end of Mission 08.
DK2 - Unlocks automatically at the end of Mission 03.
SFCR-HW - Unlocks automatically after Mission 01.
IW-80 A2 - Unlocks automatically at the end of Mission 08.
AK-102 - Mission 01, first group of enemies. Very common throughout the game.
M4A1 - Mission 01, first group of enemies. Very common throughout the game.
ATAC 2000 - Makes frst appearance at the very end of Mission 08. A bunch of soldier right at the end, at the evac point have it. Pretty common weapon among enemies towards the end of the game.
HS-36 - Mission 05, after the bridge at the start when you reach the amush site there are 3 enemies. 2 should drop this. Also appears on some crates on the bottom floor of Razad's house In Mission 08.
FAL - Mission 02, enemies will drop it all the way through the mission. Very common weapon for the rest of the game.
FDO-11 - One of the enemies weapons of choice towards the end of the game. If looking for this specifically just start the very mission some of the enemies up the first street will have it and during the rest of the mission.
Shotguns
Mos-590 - Available from the Start.
M3T - First appearance in Mission 06, when you reach the large building before the dam, there are some shotgun troops with this. Very common throughout the rest of the game.
Sniper Rifles
SR-25 - Unlocks automatically at the end of Mission 02.
CNC SOCOM - Unlocks automatically at the end of Mission 03.
M200
SASR - Mission 07, follow the officer at the start. When you get to the open area go to roof of the building to the right. There is a guard up there, and this weapon.
Mk 20 - Start of mission 4. Forty Five points it out to you saying there is a sniper rifle if you want it. There are 2 against some crates. Quite common throughout the rest of the game.
F-Edje MSR - In Mission 09 after meeting up with the 2 troops you need to guide to the evac point, the next section you make your way through makeshift buildings on the waters edge. there is a ramp up onto the top of this part (there is a sofa at the top) and then another ramp up even higher. It is under the second ramp.
Machine Guns
APEX 100 - Available from the Start.
ISR-N56 - Unlocks automatically at the end of Mission 01.
M60 - Unlocks automatically at the end of Mission 08.
RTK-74 - Mission 02, After rescuing Gold Team and setting up an ambush. Some of the next enemies you encounter drop it. Also on the bridge at the ambush point in Mission 05. Very common throughout the rest of the game.
AMELI - Mission 01, Same table as the first intel just before going down off the bridge.
PKP - Mission 04, very first encounter, check the enemy bodies for a drop of this.
(All credit and a big thanks goes to TheFlyingToaster from PS3trophies.org.)