My husband and I bought a house a few months back and our next project is finishing our laundry room. The house is a multi-level/tri-level and the laundry room is below our kitchen and above a mostly finished family room.
This is where I confuse myself. The floor in kitchen is ceramic tile, the floor in the family room is carpet. Currently the laundry room floor is cement with plans to tile the floor. The stairs between the FR and laundry room are cement- we were planning on continuing the carpeting of that flight of stairs (4 stairs). I am unsure of how to finish the stairs between the laundry room and kitchen. They are currently blue (!) wood.
I am having a bit of a hard time visualizing what you are describing, and I live in the land of bi/tri/split levels. Is the lowest level family room a finished basement?
I think I would try to make the stairs in question a hardwood. Carpet would seem out of place on that level (although I think it would be the second choice) and I'd choose that over matching any flooring you'd use in the laundry room to the stairs (tile, vinyl, etc.) You say they are painted wood now...you should be able to attach hardwood steps and then paint the risers a white or off white.