You can purchase a "false tread trim kit" or "tread end cap kit" that'll add wood to the outer 5" of so of each riser and tread. Or you can fabricate your own. Photos from stairwarehouse.com:

My thoughts are that you should probably do some more research. You can start on this website, by searching for threads that use the terms luan, joists, flooring, subfloor, acclimatization. I would wish to become pretty educated, at least educated enough to ask smart questions of your installers. I researched the heck out of my flooring project (I'm on concrete slab), and decided to purchase the flooring from a local, extremely reputable flooring store (many excellent Yelp reviews) to have leverage so that the store AND the manufacturer are more likely to stand behind the product AND their install. They do their own install, and I requested (and got) their "A Team" installers. I had visited several stores, and what I liked about the store I chose was how patient they were with answering my many, many questions. And they went out of their way to offer me options I hadn't thought of. Like this: they mitered (is it called "picture framing?) around my raised hearth--coolio! Like this: they made sure that where the wood floor meets the tile, there is no transition strip. Like this: they commented that where we have 2 steps up to our front door, that the step was rather narrow, and they could "beef it up" quite easily, making it a wider step. And they did so for no extra charge. Like this: they include for no extra charge, moving of all the furniture out of the rooms, and then back in. Like this: I chose my new baseboards, and they accommodated my request to have no quarter round, which requires more precise cuts near the walls. And those are really just asthetic concerns. You really need to start with functional concerns, which the experts here can help you with. As much as a hassle as new floor installation is, and expensive, you want to get it done right.

Can you post a picture of the stairs? A lot of it will depend on how conscious you are of things having to line up.

Dyan Weis I painted a large board to test the Accessible Beige and thought it looks flat and dirty, not to mention dark. I love Edgecombe Beige or Carrington Beige. MomMom M - My brother and wife live on the lake and have redone a home. They painted most of it Chantilly Lace and the home is beautiful Lisa Caudill Designs - I will have 2 sets of French doors (looking to the outside) flanking a fireplace with no other doors or windows on that wall. Would you paint a dark color on both the door and the trim, or just the door and do white on the trim to match the rest of the room?