I'm a bit worried that she will be ever so slightly disappointed when she sees the reality but here goes...
I use old pizza boxes from previous kits (at least three years ago now) or more recent online purchases.
Here is my March kit just after I made it up. You can see that I chose the larger of the boxes I had empty as this is a big kit. Cardstock is generally at the bottom, then papers and alphas with all the embellies tucked up in a bag so that I can rummage as I create.
In an attempt to be a bit organised and can keep track of what I have created with each kit and when pages need to be posted and where, I have come up with a small form for myself that is often also tucked into the box so it's right on hand whenever I create as well as the kit and challenge info we get from the Counterfeit girls.
All this is right there in the box so whatever kit I pull down to use, there's everything I need.
Now this works for me, but I appreciate that this isn't going to be the way for many of you out there. The main thing is to think about how you go about using your kit. I know that for me, it's never going to be that I have one kit and use it for a month before moving on to the next one. I'd get far too bored that way so having several kits working at the same time gives me the variety I need. And of course, there's all my stash too which I dip into from time to time. I try not to give myself any boundaries. This is my fun time after all.
So I hope my low-tech, stingy-style storage solution wasn't too disappointing for you and I'd love you to share with me what you do with your kits.