There are 6 shotguns included in MW3 as far as i have seen.

1.Spas-12 (pump-style)

2.AA-12 (auto-fire)

3.Model 1887 (lever-action)

4.Striker (Semi-auto)

5.Usas-12 (Semi-auto or auto, do not know yet)

6.Ksg-12 (Also a new shotgun, i currently have no information about it)

OBS: the information about these shotguns are based from MW2, since this is the game that i played the most and i felt that they were the most effective in that game.

The spas-12 is a 8 mag pump action shotgun which has 24 ammo in spare, a quite good range, good damage and reloads with a single shell at a time. This shotgun is good for single targets, and is quite easy to handle. The red dot sight and the grip increases range by a bit, and is recommended for this shotgun.

The AA-12 is a 8 round auto shotgun, which has 8 ammo in spare, so scavenger is recommended to use this weapon. this shotgun is good for executing several enemies at once, allowing for a better chance when facing 2+ enemies at once.

Model 1887 is a lever action shotgun, which has a 6 or 8 mag (i don't remember, i would appreciate correction on this, thanks!) and is good for close range, and this shotgun is special because of the akimbo attachment, allowing you to carry 2 shotguns. This shotgun was deemed OverPowered and they had to patch it, nowadays it's weaker than the spas-12 and sometimes requires 2 shots, where the spas-12 only requires 1 if you hit on the waist, or higher.

Striker is a 12 round mag semi-auto shotgun, which allows for a longer time of shooting before reloading, which could be appreciated if the enemy team is spread across 3 or 2 rooms, which allows you to kill and then run straight to the next room, without worrying about reloading.

The striker is a fairly good shotgun, has a quite good range with medium damage, it usually takes 2 shots to kill an enemy which allows for around 6 kills per mag.

The Usas-12 and Ksg-12, is still unknown to me, and information would be appreciated.

Ciao for now.