I do file boxes, which I started when we were in a much smaller house, but have liked. I do one box per size per season. Outer wear (coats and boots) get an extra. I only keep what I would actually use again, and use the rest for gifts (new and unused) or sell on eBay (new or used). I have found this amount mostly works, although I have one kid who is incredibly hard on clothes, and sometimes does not have enough, but if you're in a good loop for hand-me-downs, or have Freecycle, you'll be able to fill in the holes. I have no system for saving shoes, as my oldest boy destroys shoes before he outgrows them, and then I have just another boy and a girls, so the other shoes are passed on. I have thought about switching to plastic bins, but I like to keep the next size up on the shelf in the bedroom closet, so it's handy when the kids suddenly grows and you need something in a hurry, and I've found that the file boxes work well for that.
For switching out clothes, I have a bin in my daughter's closet (for now), and all the clothes that no longer are needed for whatever reason go in there. When it's full, I sort what I'm saving, what needs to be turned into rags, and what is ready to pass on. I keep a kitchen size trash bag of boys and girls, and when that is full, I pass it on. At some point, she'll probably want all of that out of her closet, but it works for now. GL! Have fun!