How to deal with mountain/altitude sickness in Gansu?

I would love to visit the various attractions in Gansu, but is concerned with the altitude in this province. I've been to Jiuzhaigou (at 2000m above sea level) and did not have a problem. However, upon arriving Huanglong (at 3200m+ above sea level), I felt sick upon arrival. If our family of 4 flew into Lanzhou first, what would you suggest to be our itinerary...how many days to settle in first, then move onto the various attractions, please? If my body/health allows, I would love to explore all the way to Dunhuang.

Also, how far is Xian from Gansu, to see the Terracotta Warriors after?