I would also suggest to match the walls. When you look at where the stairs meets the wall...by making it two different colors it will appear choppy looking. Making it blend in together like it is part of the wall won't make that corner and the stairs stick out like a sore thumb.

If there is a storage cupboard underneath the stairs, then I think its best to let go of the open risers. At the end of the day when it comes to stairs, I think you need to make simple decisions, don't complicate it. Sometimes spaces fuss over stairs and they can look great, but they are very impractical, expensive and dangerous. I think if you live in a house with no kids and no elderly, then you can lash out and go for something with more design risk. I think the timber stair profile shown in your picture looks great, and would work well with your vertical timber beam balustrade. However timber stairs can be noisy and quite slippery. If you are using carpet upstairs then you could consider running carpet all the way down the stairs. Don't do the half half thing. In order to finish the edge of the stairs neatly, I would edge the stairs with the plaster finish continuing from the cupboard wall, all the way up to the edge of the stairs and making an edge profile for the carpet to be neatly tucked into. By doing this you could still get the stepping silhouette which would look very cool. Then the beams could run off the plaster surface and not the edge of the carpet. Ultimately carpet may be annoying to have to vacuum, but it is a lot quieter, considerably cheaper and safer than timber stairs. Hope that helps. Good luck with it.

Victorian Ash/Tassie Oak is worth looking at but possibly yellower than you are looking for. Blackbutt is another option. Both are suitable for flooring.

It is a funny stair with a mixture of styles. The open riser is a more contemporary look, whereas the newel post, balusters and handrail have a very traditional look. Painting it white will not improve this mismatch of styles. If you paint the treads white then you will be regularly re-painting them as painted stair treads wear back to the timber quite quickly with foot traffic. From your photos it looks like you have a traditional, older style home, so you may want to consider replacing the stair with a new stair that has a more traditional look that doesn't look like a stair that was added in cheaply by a builder who had no idea when your first floor extension was done. However, a traditional stair will make your hallway seem more closed in without the open risers, and having the underside enclosed. The other option is to go very contemporary with steel and timber which is visually lighter and is in contrast with the rest of the entry hall. It is a really important visual element to the entry of your home and a coat of paint is not going to fix its problems. Best of luck with your considerations, Dr Retro of Dr Retro House Calls