Not sure if I understand what you mean but there will be no AK (just an "automatic rifle" that shoots "automatic rifle ammo"); and a sniper rifle will shoot different ammo. I guess you already guessed how it's gonna be called.
Some games (e.g. PUBG) have the Tokarev TT-33, the Mosin-Nagant, the M24 sniper, and the AKM using the same ammunition - because they are all 7.62mm caliber. Even though they use 4 different type of ammunition IRL. That's what i was referring to. 7.62x54mmR =/= 7.62x51mm =/= 7.62x39mm =/= 7.62×25mm.
Using generic ammo specifically for the weapon is reasonable, though.
Your character will be arrested upon getting caught = game over.
This is playing as a police officer? They use firearms when needed. And thus:
Is not strictly accurate. Every police officer will have mandatory training with at least sidearms, and will be issued some form of automatic pistol. Also, non-specialized police generally carry one sidearm and one long arm. Historically a pump shotgun, but many departments are moving over to AR-15 style rifles. Sometimes SMGs like the MP5, but those are also generally more for specialized units like SWAT.
In the event of SMG, they almost universally are chambered in the same round as the pistol. This is done so that the same ammo can be used. If you do the "pistol, sniper, shotgun ammo" route, I suggest against SMGs entirely.
Overall, an ex-police officer would allow for more relaxed RoE while increasing consequences for combat. Dunno how well it would end up working in the story though. If you do go that route, remember that possession of a full-auto firearm is a federal felony in the US. One with particularly bad consequences in any place that has firearm licensing requirements. Just something to keep in mind if the character has to stay well within the law.
Yes, I know I am getting a bit detailed about this. It's just one thing that really bothers me about guns in games.