There are 6 gun classes (or types of guns) in the Division, as follows:
- Pistol
- Submachine Gun
- Assault Rifle
- Marksman Rifle
- Light Machine Gun
- Shotgun
All you'll need to do is grab a kill with each type at some point in the game. I would not recommend going out of your way to spend credits on weapons you don't want just to do this. Keep playing and you should get one of each relatively quickly through mission drops.