I use freezer ziplock bags with 250 to 500 rounds per bag, with the info written on the bag, and they are stored in either 5 gallon Home Depot buckets or I have a bunch of those big Rubbermaid outdoor style trash cans in my basement and the ziplocks go in there. I think they are 40 gallon trash cans, or something like that. Not the real tall ones with the wheels embedded, but the round grey ones with lids that snap on. My thinking with that is that if we get some flooding in the basement (hopefully never will) the trash cans are high enough that hopefully water will not rise high enough to over top the lids, and even if it does, hopefully the ziplocks will keep the ammo water-tight. The home depot buckets I use are up on a table, so hopefully water will not reach high enough to get in them. They are heavy enough (with their cargo of ziplocks full of ammo) that I can nudge them around the table but can't really pick them up and move them due to weight and my reduced leverage since they are up on a table.
For going to the range, I use the 50 cal ammo cans because there is enough room for magazines, an UpLula loader, and a ziplock or two full of ammo for that range trip.