Building a shelf in basement renovation. Need help

Is the shelf going to sit inside the wall?

Yes. It will be going inside the wall.

Is that some sort of water/heating system there? Are you sure you want to box it in? Is anything likely to need maintenance?

#1 The underside of those stairs was suppost to have 5/8 fire rock to meet code.
#2 Looks like you may trying to build a wall without a pressure treated bottom plate. (can not really tell about the whole wall because picture was take to close up)
#3 Really should have built a wall first on the side of those steps so your not just looking into the area where the heater is as you come down the steps.
#4 That storage area is going to need a door with louver for supply air for the heater, or at least a vent in the wall.
If I had to build what your trying to do I would have framed it as if I was building a closit, sheetrock it then do one of two things, build a shelving unit and slide it into the space or just add some shelving.
If it was mine I would frame the opening so a standard sized bifolding door would fit.

Yeah I am building a wall on the inside of the stairs before I finish this.

The bottom floor plate is all pressure treated lumber. The reason you don't see it because the picture is up close.

There are two 24" bifold doors down the wall in the middle to reach the hot water heater and condenser. I also have built the wall a few feet off the cement wall to allow access to the electrical panel.

Yeah I am just trying to get a handle on this as my wife is driving me crazy as I originally wanted to at an angle place Sheetrock and seal that part off

Thanks again
Jp

Simple,handsome cabinet style shelves can be made up like open boxes---use cabinet ply if you wish to stain them---slide lem into the openings and nail them in---Trim after the drywall is in---