Oh wow, that’s brilliant! I’m really jealous. ;)
I’m finding it difficult to picture what that amount of yarn would look like in terms of its volume. How many balls is it?!
For me, the most important thing is that the yarn remains relatively free from dust and other yucky things. Then, I think it’s important to store it in such a way that you don’t have to rummage around and throw everything out onto the floor just to get the one bit of yarn you want!
I don’t have an awful lot and so don’t really need to sort mine, but I store mine in this bag as it is very light, zips up and is sufficiently large (about 60cm on the longest side). Bags like that come in a variety of sizes, and as the bag itself is very lightweight, it doesn’t really add bulk to the storage! It also keeps its rectangular shape, and can be neatly stowed away. They are also very cheap (that one I have is made out of recycled plastic bottles!).
Maybe what you could do is categorise the yarn (perhaps by colour, type or by project and what yarn you think will get used together), and then put it into some sort of zip-up storage bag, that’s a fairly regular or sturdy shape. Just thinking of larger storage solutions, maybe one of those transparent airtight bags that you can use to store large blankets or rarely worn clothes in, then you could slide it under a bed (if your bed is that sort), or store it on top of something (e.g. wardrobes) – you obviously wouldn’t need to stuck all of the air out! If more rigid storage would be better (i.e., something that you can stack up, and needn’t hide away under/on furniture), perhaps try some clear sturdy boxes, like this sort of thing – these are just shoebox sized plastic containers, or you could get something a little bigger, like one of these .
Best of luck finding a good storage solution!