Militaries excess and dispose of their unused ammo after set time periods, because they can, and consider its cost as part of doing business.
If lives depend on the ammunition being "good", get rid of the old stuff if it is within your means. For the government, it is clearly within their means.
I store in different kinds of containers. But I mostly use US Army metal ammunition cans, and plastic ones with seals. For the most part, I label the cans by caliber. The ammunition gets stored inside it's original box. Any reloads are placed in plastic boxes with load info written on them as well as the number of times the brass has been reloaded. Even then, I try not to mix ammunition of different ages even if it is the same load.
I do not like to dump any kind of ammunition (including 22LR) into loose containers unless it was purchased that way. In which case, it still stays in the "factory" containers.
I try to record the Month/Year purchased on the box.
Added: When I first started out, I had two 50 cal ammo cans for storage... 22LR and "other". Times have changed. I never stored shotgun shells in metal ammo cans. I have a large wood military box for that.