The $2K price for 470sf AND 11 stairs is a GOOD PRICE. The refinisher is right on track with the estimate.
You are welcome to learn all the tricks of the trade for wood floor refinishing. Right now you probably have the time. Your research time investment should be a few hundred hours. That includes all the youtube videos you can stomach. You will also contact the manufacturers of the product you are interested.
If you were to use Loba 2K Supra AT (10 minute working edge = decent for water based):
1. 1 Gallon of WS EasyPrime = $100 = 450 - 500sf (you might need two gallons just to be sure)
You will apply a single coat over the entire floor once the sanding has been completed
2. 1 Gallon of Loba 2K Supra AT = $195 = 500sf for first coat. You WILL NEED two gallons to finish this floor.
3. Microfibre rollers = $10/per head = 3 heads
4. Painter's pole = $20
Sanding equipment = 3-4 days of rentals (your floors need ++ work...there is PLENTY of wear through...the poor things needed love 10 years ago)
Sanding pads = double digits worth of product. You will need 3 different grit levels (eg. 60, 80, 100).
Moving all the furniture and then staying off the floor for 10 days = normal.
Q