Well it sort of depends on just how many miniatures you have that determines how important organization is and what kind of organization works best. 25 or 30 years ago when I started I kept them in a small, old fishing tackle box. At one point I had a small wooden box that I made several balsa trays for with individually cut foam for each mini but that was just for PC figures, not monsters. Eventually I graduated to a small-parts cabinet and started just piling a lot of the figures in the drawers, while the individual PC figures that I was particularly proud of wound up on a wall display made from a printers tray.
I almost never have kept them on shelves. Too many cats or small children to knock them around, eat them, etc. Besides which, well over half of the games I've run have been away from home so my collection needs to be at least modestly portable.
Now I have six parts cabinets, four of which are quite large, holding some 1500 or so miniatures, about 1100 of which are the new WotC plastic minis. I haven't really thought of any better way to organize them though as it is a lot of those drawers are CRAMMED full and I had to put labels on all the drawers so I could theoretically know what's where.
How I make use of them is now somewhat varied. Sometimes I will pull out minis that I know I'm going to use ahead of time. Sometimes I will simply search for what I want when it actually comes up. Sometimes I will go through them simply to keep myself familiar with what is where and get ideas for what I might want to use.
When I finally win the lottery I'll be able to build a fully dedicated gaming room with rotating shelves to display all my minis of all sizes because I won't need to keep them mobile anymore. Someday...
Oh and the PC-type figures I divide mostly by class, fighters in this drawer, wizards there, clerics there... Humans and elves tend to get collected together in that regard because they can easily substitute for each other. So if I need 30 human bowmen but only have 12 then the elven bowmen will stand in. Dwarves and halflings get divided as their own category, both because there aren't enough to subdivide them but because of how they get used. It is seldom a matter of "I need 3 dwarven clerics" but "I need 3 dwarf miniatures of some kind for this encounter".
It's less necessary now that I have so many, but even now it is STILL occasionally required that one type of miniature substitute for something completely different. "These orcs with spears are actually the hobgoblins with swords and the ELVEN bowmen are actually the HUMAN Crossbowmen. Everybody got that straight now?"
