Hi everyone! This is in one of our AirBnBs that we own. These stairs used to be floating stairs but we closed them in initially to limit liability with guests.  
Now, we're wanting to completely close in underneath this staircase to add an owner's/cleaners storage closet to store extra materials - linens, decorations, toiletries, etc.  
I plan to frame out the existing area, then drywall floor to ceiling (covering all but the far left 4 of the white 2x4s that are attached to the stringers), and will drywall the inside of the staircase to match. The door to the storage closet will be on the far right where it's the tallest area under the staircase.  
I'm really wanting to build drawers for the bottom left triangular area under those far left 4 2x4s that will still be visible - still undecided. If we do decide to do drawers, it will have to be at a later time though, but I plan on having the framing/structure there now and can remove the drywall later to build/install the drawers.  
We also plan to mount the TV to this wall once completed as well.  
Any/all advice on this project is welcomed!  
My questions for the more experienced people:  
\- Where would you start? My thought process is to frame in where the wall and door would go, including 2x4s along the floor to attach the vertical boards to. Then build out the door frame itself, then drywall everything in, etc. Am I missing something in the framing process?  
\- Would you suggest I do a hidden door (I'm thinking we may do vertical shiplap on this wall and could have the door hidden that way), or just put in a regular door, no shiplap?  
I'm sure I will have more questions based on responses, but trying to plan everything out now so I can gather materials and start working on this later this week. TIA!

Closing In Under Staircase For Storage