I keep mine loose, in surplus .30 cal ammo cans. They're robust and stack well.
All of the ammo in one can came from one lot, and I have the section of box with the lot number in a clear label holder on the underside of the lid. Mailbox numbers note the caliber on the side and top.
I have a few .50 cal cans as well, mostly full of .22lr valuepacks and minimags, odd boxes of this or that and carry ammo. .50 cal cans get heavy, so they don't move unless I'm actually moving, which I hate doing...
.50 cal cans aren't so bad if you leave ammo in the factory box. So, if you keep a small amount of ammo on hand, they wont be so bad to move around. If you buy in bulk, use the .30 cal cans, and you can ditch the factory packaging for more room.