Just store them in the box, especially if it is temperature controlled. All that old surplus ammo still runs pretty well despite less than ideal storage.
A single stage has a lower cost entry point and with many of those rounds being more low volume shooting it would let you get your toes wet without dumping a bunch of money into a hobby you don't know you like.
I wouldn't want to load 5.56 plinking Ammo on a single stage unless it was for...