Are you looking for a ceiling light, or wall lights to shine on the steps?

 

If Ceiling, it should be shining down. If you want accent lighting along the stairs, so you can have the overhead off, if going from living area, to living area, you would have to cut into the drywall to pull the wiring for those. Really need a better picture showing the whole stairwell, not just the last step & landing.

 

A ceiling light will give much better lighting to the whole staircase.

 

For stair lights specifically, LED strips under the overhang of each step are pretty good. That would light the top step, but not the landing itself. A ceiling light would be best for the whole area though.

 

The landing has a ceiling light that does a pretty good job, when and if it is turned on. I was looking for some always-on accent lighting, probably DC? Problem is I don't know where to place it where it would better define the edge of that first step. The first one is the tough one.

 

Maybe talk to a real lighting specialist, not someone in a Orange apron.

 

LED strip under the overhang of the landing would probably work best. It will look nicest if you do it on every step, but that's a lot of work.