u/Alphabrett

I'm trying to design a frame for steps up to a bunk bed that I'm making for my son.

I've done a few simpler woodworking projects before such as shelving units and a decorative box frame for a household battery, but I'd still count myself as fairly novice and this is my first bigger project.

Am I missing anything glaringly obvious in the design in terms of structural stability? I'm planning on putting shelves under the steps accessible from under the bunk bed.

What dimensions of timber would be best for this?