In your situation...If i were you, and I was commited to a complete drain/refill, here is what I would do.
Drain.
Refill. Circulate the water for an hour or so. Then test.
You will get FC of close to 0, CYA of 0, PH of x.x and TA of x.x. And since you have a plaster pool, you'll need to worry about CH as well.
I would then get about half a gallon of good ol bleach in there.
I would then use pool math and calculate how much CYA you need. 20,000 gallons at a CYA of 35-40 is what I would shoot for at first. You're probably looking at ~6lbs of Stabalizer. I'd start out with 5lbs and wait a week and then test it to see what it actually made your CYA. Best way to add CYA is to pour the Stabalizer into an old sock and tie a string to it and let it hang in front of the pool return till it dissolves. CYA wont show up on your test immediately. It will take about 5-7 days to register.
This is what you need....And you'll need 2 of them.
http://www.walmart.com/ip/Clorox-Pool-and-Spa-Chlorine-Stabilizer-4-lbs/41466055
Adjust your TA and PH to suit.
Then every day for the next month or 2 months i would be out there testing and adjusting my FC to stay right around 4-5. And making sure my PH was around 7.5. You'll get a good feel for how your pool reacts to different things.
My pool looses about 2ppm on FC every day if its uncovered or being used. If we dont use it and it has the solar cover on it, it holds the FC for 2 days...sometimes 3. My PH rarely moves from 7.5. And if it does, it drops to 7.2 and i just turn my jet up and let it aerate to get back to 7.5.
I keep my CYA at around 30 for the beginning of summer because i know i'll be taking a week in june and a week in july for vacation. I then use pucks to control the FC during those weeks. They add CYA. Usually in August, my CYA is close to 40 becuase of this reason. But if you stay around here and read up, you'll understand that and be able to adjust for it like I do.
Good luck. Stick around. These guys are VERY good at what they do. You'll have the clearest, cleanest, most sparkling pool in your neighborhood....And not to mention, the cheapest one to maintain.