Awesome news -- finally!! Congrats!

In a 20K gallon pool, 3 lbs. of stabilizer will add about 20ppm of CYA.

Ranges:
Chlorine --- based on your CYA level. See the Best Guess chart in my signature below. (If you let the cl dip too low, you'll risk an another algae bloom.)
pH -- 7.2-7.8
Alk -- 80-125
CH -- not needed in a vinyl pool

Stay in these ranges and yes, you'll be good to go! Test chlorine daily, pH once or twice a week, alk every 2 or 3 weeks.

Enjoy your pool!

(For reference, in your pool, each quart of 6% bleach will add about 0.8ppm of chlorine. Use that to help you determine how much bleach to add each evening when you test.)