Projectile weight - Heavier bullets would create more recoil, have better penetration, and keep energy over long distances. Lighter rounds would recoil less, have better accuracy over longer distances but not be as good for penetration.
There's no recoil in the engine, but it could increase spread. This touches on two of the major drawbacks of weapon mods: they can't be removed and they can only have 1 effect each. IMO a silencer, for example, should make the weapon silent, increase spread and slightly decrease DAM. You should also be able to add/remove it as required. Of course, one necessitates the other: if you couldn't remove the silencer you'd want to carry a second, unsilenced copy for the improved stats, or if there are no penalties to mods there's never a reason to remove them.
Powder charge - A light load would create less recoil, produce less stress on the weapon. A hot load would create more recoil, push the round faster for better penetration and stopping power, and produce more stress on the weapon.
Isn't this how +P loads work?
And I think the game should allow players to make critical mistakes, like over charging a round and turning a hand cannon into a bomb! Exploding, destroying the weapon and possibly harming the player's character in the process. Crippled limb anyone?
Losing the Gobi or All-American because of a misfire anyone? No thanks. It would be hilarious to get a misfire on Annabelle though (assuming you had a recent save).
As for other ammo types, I can't think of anything off-hand. I practically never switch ammo types because non-standard ammo is generally hard to find (especially for auto weapons) and primers, cases and powder are too hard to find in sufficient quantities. Given the setting, I think every merchant should have heaps of this stuff in stock each refresh, but in practice they seem rare, and you practically never see a vendor with all three.
Actually something that would be handy is the ability to craft missiles, 25mm and 40mm grenades, etc. I don't think there's any recoverable material from firing a grenade though (eg a case), so it may be tricky.
Also the ability to break down/combine explosives to create others, eg C4 + 3 tin cans + scrap metal <-> 3 frag grenades, or similar.