I think plastic containers are a bit like rabbits... except they're rabbits with a bad sense of direction and tend to get lost.

We have a large-ish collection of Ziploc containers. I like that they're cheap, light and recyclable when done. They are also quite durable, even with microwave re-heating, and don't get brittle (i.e. the plasticizers stay in the plastic so they stay soft, rather than leaching into our food and getting brittle). Mind you, I only heat my leftovers until they're nice and warm, and not boiling hot. I purchased an
Ikea Trofast tall storage unit to sit in a spot between DD's desk and the wall in the kitchen, and it holds her school stuff in the bottom half, and our most commonly used containers in the top half. I basically have one medium bin for our main matching Ziploc containers, another medium one for our other random containers (like the 1lb moisturizing cream tubs I use for freezing broth in) and two shallow bins for lids and other bits and bobs. (I also have one for DS's "school" stuff - math manipulatives, art supplies, etc. Trofast is cheap, effective, and mostly wood.)
It works pretty well. We do have a few other stashes - like all the takeout containers, and the larger containers that seem so useful... It takes a lot of gumption for me to get rid of any of these things!
We're also slowly accumulating Pyrex and Glass-Lock containers, but I still prefer the lighter-weight and less fragile plastic ware.

So far those are living on a shelf with our Pyrex and Corningware baking dishes.