Well, Smitten, those "beams" are called joists. Pictures will tell how large and what the spacing is (16" or 24" are common). The first video I provided has the stair kit being sintalled in a hallway with the kit running parallel to the joists. The second video series has the kit perpendicular to the joists (more complicated). As Neal correctly points out, the framing he used in the 2nd video series was weak -- should have been doubled to carry the ceiling load.
I have installed a wall door such as you describe. It worked nicely and was easy to do with 2x4 framing and a plywood door. Since you are going to store stuff, remember everything we have said so far. Also, the size (H and W) need to allow for large boxes too. The stair kit provides a large opening so this is not an issue.
Get started so you daughter can have a place to live!