I would look at something chambered in 9mm or 5.56 since there is plenty of it for military purposes.
I see a lot of folks use that reasoning.
However, unless you're actually in the .MIL and know what the ammo storage areas are for local armories etc. are, (presuming they're not defended) and how ammo distribution works... the mythical stocks of these "common calibers" would take some time to appear through the black market etc.
IMO, you're one of the few who'd have an idea of what to do and how to procure some of it.
If things are bad enough I'm getting a significant amount of common .MIL calibers as "battlefield pickups", I probably ought to review my plans as to why I and my family are in such a dangerous area.
Having diversification of firearms in your armory into common calibers, 5.56/.223, 7.62x39 and x51 NATO, 9mm, .40, .45. .38/.357 is probably not a bad idea for barter, found ammo etc. it might extend your ability to shoot back, perhaps for years.. But most folks will only ever have what they've stored up in advance.