Safe bets:
.22 LR
.223
7.62x39
.30-06
30-30
9mm
45
40 S&W
Just to name a few.
7.62x39 has been popular in the USA for maybe 20 years, mostly because the rifles firing it are so cheap that everyone has one. .40 S&W has been around maybe 25 years, and is largely practical for law enforcement et al. The rest of the cartridges are old enough to fit the "always available" category, but I still don't get what you mean by "safe bets", given how simple it is to make ammo for cartridges most people haven't even seen. When you're talking about something like the .375 Ruger, which is widely available even on an island in Alaska, like where I live -- it's fairly hard to figure out what the issue is about. Certainly can't be whether or not they're available, because they are.
But hey -- use what you want. Just don't be fearful about acquiring ammo in the US...it's more available now than maybe ever. Certainly more available than 40 years ago.
Dennis