We just went through this last week. We used an oil based finish on our floor and we are very happy with they way it turned out! We had planned to use a light stain on our red oak floors. After our cabinets went in the stained sample we had looked too close to our cabinet finish. We decided to use a clear finish. We are so glad we did, it is just the color we wanted. The just sanded wood is very light. The clear finish came out quite a bit darker than it looked like on our small sample piece. Think of how water changes the look of a rock--the same thing happens when you put a clear finish on dry wood.

I am chuckling here about the MCM vibe and light flooring. MCM often had light floors or even not wood floors at all . I do agree the basement can have a different floor .I usually like the stairs to match the floor below so like the main floor and the stairs going up and in you case the cork on the stairs would be my choice .As for the actul color of flooring in the main floor you go with a color that works with your stuff and honestly floor color in wood always needs to work with your stuff not some trend.

Thank you for all the suggestions. We are in the final stage of making our decision for our flooring finish and leaning heavily toward Rubio Monocoat "Pure." Pure would be less honey/blonde/champagne than our original inspiration and more on the amber/red side (We tried a sample of the Pure with Pink Blocker pre-treatment but the swatch unfortunately has a visible green tint.). One thing that we appreciate about the Pure finish is that, barring any "design related preferences," the red oak wood really looks beautiful with this finish on it. It brings out a depth and spark of light to the wood. There are some photos of Pure on red oak online that we like, and others we don't like so much. It is difficult to predict whether our finished floor will look more like one vs. the other. For example, we like this example of Pure on red oak from the Rubio Monocoat website: And we like this example of Pure on red oak from this website https://theflooringartists.com/projects/rubio-monocoat-pure-red-oak/ We don't like these examples of Pure on red oak as much (see below). Maybe it is the characteristics of the specific grade of wood itself, or some aspect of the application:

I think you can easily mix birch in with your maple and oak as long as the colours work together and aren't abutting one another. Birch is a hardwood with a tight grain, not dissimilar to maple once stained. Oak has an open grain and generally the graining is quite pronounced when stained, moreso than the maple or birch will be. You could consider painting the pine on the steps to limit the colour changes throughout. Pine isn't a great choice for stairs or flooring because it is a softwood and can ding and get gouges much easier than hardwood. Pine generally doesn't take stain well so you'd have a hard time getting it to stain and match any of your other flooring choices. I would be more concerned about finding colours that work well together and focus less on the wood species. For cohesiveness try to stay with a similar size plank in width.