Hello everyone. I'm going to be installing hardwood floors in my currently carpeted home in the near future. I will also be replacing the carpeted stairs with hardwood. I'm not sure if I want to rip up the carpet on the stairs and overlay the existing stairs with hardwood or if I should rip out the entire staircase and have another one built. What are the opinions on this? Also, should I install the flooring first or the stairs first? Thanks.

It does not matter what order you do the floor and stairs.

Why would you want to build new staircase? Unless you want to change the walls , even if the stair case squeaks it can be reinforced but building a new one would be a big project.
I would definitely take of the carpet and do all the prep on the staircase and the sub floor, I have started to sand the staircase roughly with 40 grit using edger just to even everything up, staircases tends to have a lot of pain on it or glue.
After all is prepared it does not matter what you do first.

Yes I agree, It does not matter what order you do the floor and stairs.