I'm confused about what your floors and stairs are currently. But here's what we did. On the main floor we have cherry floors, and we put pine on the second floor. We put cherry treads on the stairs (and painted the risers white to match the trim). The landing upstairs, which looks like the top step from below, is pine. I think you want continuity between the stairs and the first floor, either by doing something like this or doing what floorguy recommends.

I recently went through this carpet->wood on stairs conversion myself. We had 17 stairs + a landing and an extra step up to the landing. I used pre-finished 5" maple planks (engineered) on the treads to match the wood in the rest of the house. We bought pre-finished nosing for each step ($$$). For the risers I used 1/2" birch plywood painted white (nice contrast with the dark wood). Overall, I'm happy with the end result. However, it wasn't easy and took a long time. 1) it's a lot of work, and, if you don't put some thought and time into it, it will show 2) Walls and stairs are rarely straight, perpendicular, parallel, or aligned in any direction to make this job easier. Each and every cut will be unique 3) Our staircase has a stringer on each side - no balusters to worry about, but that doubles the number of unique cuts to make 4) pre-finished nosing is expensive. Our steps are 42" wide. The nosing comes in 78" sticks. I didn't want a splice in the nosing, so that meant one stick for every stair 5) After we started, I found some places online that sell one piece treads. I'm not sure that it would have been cheaper than fitting multiple planks on each step, but it would probably be a lot less cutting. 6) with 17 steps, the less trips down to the saw and up to test the fit on the top step the better. Of course the top stairs are probably going to be the ones hardest to get right I found the hardwoodflooringtalk website to be very useful during our entire install. There are several guides and a busy message forum. I recommend you (or DH) spend some time browsing it before starting. Unfortunately THS won't let me post a link to them here, but a google search for "hardwood flooring talk" should get you there. Good luck!

Courtesy of another GW'er, I've found another source for hardwood stair treads at a much more reasonable price. Orubuis--I don't remember the specific product that I used on my stairs but it was some kind of penetrating tung oil. Wasn't Waterlox because I haven't used Waterlox yet. But Waterlox can go over stained wood--that much I know. Just be sure it's an oil-based stain. Another factor with wooden stairs is the noise issue. For that reason you may want a runner. My stairs are back stairs & get tons of abuse. So, yes, they have scratches. But the finish isn't worn thru, chipped, peeling, etc., all the things that can happen to film forming finishes like varnish, poly, etc. And they're easy to sweep down and clean with just a swipe of a rag vs hauling out a vacuum and living with the plain nastiness of carpet, esp. with the location & use of my back stairs. Here is a link that might be useful: Hardwood Lumber (stair treads)

We have hardwood on our main floor and LVP on our stairs down to the basement as well as on the basement floor (over cement). When the LVP was first installed on the stairs (it's been a little over a year now), my husband thought the "lip" part of the stair treads (the bull-nosed edge piece) was not installed perfectly flush and secure on several (I think 4) of the treads, so I wonder if that is not uncommon and is what your flooring contractor is worried about. I didn't even notice it, but my husband is a perfectionist and it bothered him. Rather than complain and have the installers come back to address the issue, my husband fixed the issue himself. I think he used tiny little nails (with no heads) to better secure the edge pieces to the adjoining LVP pieces, and I used dots of acrylic paint from my art supplies to cover the bitty nail holes. We have never had a problem with them since and we are up and down the stairs many times daily so they get heavy use. Just wanted to mention our experience in case that makes any difference for your decision. I don't regret using it on our stairs. We picked an LVP that coordinates pretty well with our upstairs hardwood in color, just a little more rustic which fits our basement vibe. We didn't want to introduce yet another type of flooring just for the stairs.