I put my 12 x12 paper in plastic envelope like this:
Then I store all of them in a tote. Mine has wheels and an extendable handle. Love it. I use those envelopes for stickers too. I can store my pens, scissors and other tools in my tote. I got it for Christmas 2 yrs ago.
This is similiar to what I have.
I don't have a HUGE collection of stuff but this keeps it all together.