I am in the process of remodeling the basement, and one part of it is to update the stairs. In basement, I am planning to have this cold brown tone vinyl floor (https://www.homedepot.com/p/MSI-Provance-Gray-7-13-in-W-x-48-03-in-L-Rigid-Core-Luxury-Vinyl-Plank-Flooring-23-77-sq-ft-case-VTRHDPROGRA7x48/312591261), and one main floor I have water based red oak floor (light pale yellow). The stairs are plywood, but they did a good job with the bullnose and everything.

What should the stairs be stained to? similar to lower level or main level? Not a big fan of carpet on stairs, especially going down to the basement, feels like a hazard and nightmare to clean.

Any advice would be appreciated!

water based floor: main living area + second floor

vinyl plank flooring for basement: