Should I keep the box and stuff?

Quick answer, yes.

When a doll is first ordered, the company generally sends the doll packed in an official box with pillows for protection (sometimes a padded bag or formed foam) and the doll's certificate of authenticity. Most collectors consider all of the company sent items as part of the doll. Should you decide to sell, keep in mind many buyers will consider these things a must. So keeping them around and in good condition adds value to your doll.

CoA's are actually more important than a original boxes, as they can prove your doll's ligitimacy. If you keep nothing else, keep that safe.

1/3 dolls' boxes can take up a lot of space, so if you need to, some boxes can be folded down and tucked away for safe keeping. I actually keep mine in tact and use them to store all of that doll's accessories and clothing.