Keep things as simple as you can.
Light pistol ammo.
Heavy pistol ammo.
Light rifle ammo.
Heavy rifle ammo.
Shotgun shells (shot).
Shotgun shells (slug).
And that's it apart from the odd barrel loaded grenade or rocket.
For pistols, anything over .357 is Heavy. .357 Magnum should also count as Heavy.
SMGs use mostly light pistol rounds.
Most rifles use Light Rifle ammo, especially assault rifles that are less than 7.62. Anything larger is Heavy Rifle ammo.
Machine guns mostly use Heavy Rifle ammo (in reality, many use slightly different loads for the same caliber, but it's not worth it unless you're worried your players are going to hoard ammo for their HMGs). Miniguns use Light or Heavy Pistol ammo.
This isn't very realistic, but it will save you a ton of bookkeeping, and will make it easier for you to distribute ammo to your players so they can meet the challenges you want to throw at them.
If you want to simplify things even further, just create a variety of generic gun types and give them stats.
Hold-out revolver.
Hold-out semi-auto.
Light revolver.
Light semi-auto.
Heavy revolver.
Heavy semi-auto.
Machine pistol.
Submachine gun.
Double barrel shotgun.
Sports shotgun.
Semi-auto shotgun.
Fully automatic shotgun.
Varmint rifle, semi or bolt.
Hunting rifle, semi or bolt.
Sniper rifle, semi or bolt.
Anti-material rifle, semi or bolt.
Assault rifle.
Light machine gun.
Heavy machine gun.
Minigun.
That should cover 99% of your actual weapon category needs. Feel free to add small modifiers to any given generic weapon to make them feel different.
"Long barreled heavy revolver adds 10% to its range", "Sawn-off double barrel shotgun has 75% less range, but deals twice the damage" or stuff like that.
With guns you either go simple and generic, or full blown /k/. There is no sensible middle ground that will please everyone.