Depends on the condition of the hardwood now. Also depends on the floor prep needed to lay the vinyl floor. The costs could be very close. Your question sorta sounds like "should I fix the Ferrari or just buy new Chevy?. IMHO I think I would try to keep the wood if at all possible.

Thank you both for the advice. We have pulled up 2/3 of the carpet in one bedroom and thankfully, it's already painted (particle board) so we'll just prime it and then re-paint it. I believe it's double construction. We're going to pull up the carpet in the living room today before we move all the furniture tomorrow and while we know that there's hardwood floor under there, I hope there are no other big surprises! We've decided to prioritize the living room carpet and packing and moving while leaving the work on the bedroom and hallway floors to after we move in. We might even spring for hardwood floors after all.

While yes, it would be possible to use a different sander in those areas, I wouldn't head that direction if I had other options. First, the price quote was for doing the entire interior of the room with the big machine. If a smaller machine was used, the labor cost would increase and the refinishing will be more money. If you are looking to use stain on the floor, different machines remove material differently and if the surface isn't machined with the same equipment, it won't absorb stain consistently. It isn't just the grit used, it is the brand of paper, the type of abrasive, the speed and direction of movement, and any other seemingly unimportant detail that actually will impact the finish surface. If you have ever seen a floor with a darker or lighter perimeter, that is the result of trying to stain two unequal materials. I had noticed the picture frame effect on floors over the years and didn't know the cause the first few times I saw that, typically in properties for sale with listings touting newly refinished floors. The darker the planned stain, the more noticeable those surface irregularities that become glaring issues. Without stain, those issues will not be nearly as obvious and perhaps not visible at all to the untrained eye. Another concern is movement of the floor while being sanded. If the floor has boards not securely attached, the sander will bounce slightly and leave horizontal lines or longer waves in the surface. That is usually described as chatter and is sometimes visible on wood moldings as well.

Would you say it’s more of aesthetic thing then, not that one way is more complicated than the other? I do see the value in the solid wood stair. I just wouldn’t take off the carpet as long as I’m in the house because a family member’s disability makes him prone to tripping. I don’t see us moving in the next 5 years. But it’s not like wood could be added to the middle of the stair later, so I guess I have to think about it.