I want to paint the walls above my living room stairwell. The stairs are four feet wide. I'd like to cover the stairwell with wood boards so I can stand my ladder on the boards to paint the walls overhead. The length of the boards would be about 4' 5". How thick should my boards be? How wide should they be? What type of wood would be the best? I am about 165 pounds.
Regular framing lumber will do what you need. You will not want to place a ladder on individual 2Xs that make up your scaffolding. The deflection on one 2X will feel enormous when you are on the top of a ladder. 2X4s are cool as long as there are no large knots, and you fill the area. #2 grade 2X needs to be watched for this. Don't even use #3 grade. I have seen 2X6s with 2" knots in them that would render them useless as a walk plank. All said, please be mind full of the condition of the wood used for walk planks. Since you are putting a ladder on all this, unify the surface with a sheet of plywood (1/4" will work in a pinch with a solid fill, if you spaced 2X6s, use 1/2") cut to fit within reason, 3' wide or larger will work and as long as feasible. Believe me, you will not want the ladder to find even one gap big enough for a ladder leg to slip through.
Wood 2x4s should be adequate, especially since the ladder will be distributing the load to four points.
However, to allow a reasonable amount of ladder walking, non-precise foot placement, and protect against random defects, earthquakes, etc., 2x6s or larger would be entirely appropriate. I bought a 20' 2x12 years ago for such a project and have made all kinds of useful steps, stools, and other furnishings with the pieces of that temporary scaffolding.
Regular framing lumber in good condition held together with boards running perpendicular every 2' or less would work well.
Have the boards underneath in "on edge" position would work best.
Here you can see a different version where we have 2x10 planks with a 2x6 "strong-back" (on edge) screwed to the bottom to keep the deflection to a minimum:
And from underneath