We have 3 fake trees, the first one we bought a large plastic tote box for years ago and it fits easily in there. The 2nd one is the Disney tree and is kind of skinny, I bought a tote for it too. Since the tree is smaller I can actually fit it, the tree skirt, monorail (in box), a huge Mickey snowglobe and a few smaller items inside. The new tree this year still has only the cardboard box it came in, I will be on the look out for a tote soon though because it took 2 people and everything we could muster to get it into the box and closed. We taped it shut and I am hoping it will stay that way!
I like keeping them in totes better anyways, I feel like dust and such can get into a cardboard box easier that a tote box with a lid snapped on.