There are over 600 individual miniatures, and depending on the extent to which you have bought into this, I could easily see where you would have too many to display. So assuming you don't want to display them, but rather need a place to keep them where you can get to them quickly and transport a few favorites...
Go to AC Moore or Michaels, or some other craft store and buy those cheap little cases that crafters use for beads - should be like six bucks each. I like the kind that has configurable compartments so that you can create a big section for orcs or undead, and single compartments for your Blue Slaad or Iron Golem. I keep one of each type of mini in said cases (I have seven), roughly organized by creature type: Fighty Heroes; Casty Heroes; Specialist Heroes; Villanous looking humanoids; Goblinoids; Kobolds; Lizardmen/Trogs; Giants; Gnomes/Halflings; Green Miscellaneous; Purple Miscellaneous; Red Miscellaneous, Winged Miscellaneous, and so on.
For hordes of commons, I have plastic baggies in tackle box for extras that are good to pull out when you need a bunch of Dwarves or Drow or something and you don't care if they all look alike.
If they're too big to fit in the boxes, then stick 'em on a shelf, where you get to explain to your normal friends - "Why that, that is a detailed representation of an Aspect of Tiamat, Queen of all Evil Dragonkind, and no it would be far too expensive a toy for my son..."