Common Misconception of Yixing Clay Teapots
1) $20 new "Yixing teapot"
Most $20 newly made "Yixing" teapots use clays with added chemicals. They can be harmful to your health. You would be better off using porcelain teapot or Gaiwan instead. I would spend at least $100 or $200 buying an old Yixing teapot from a trusted source.
2) $50 new Yixing teapot of "DaHongPao" or "ZhuNi clay" (Not Easy to Identify)
ZhuNi clay are pretty much used up and DaHongPao clay is more so. $50 Yixing teapots of "DaHongPao" are made of bad clay with added chemicals. Authentic Yixing teapots of ZhuNi or DaHongPao were almost always made in the 1980s or earlier. Generally speaking they should cost $400 or more.
Chemical Teapots (LEFT) vs DaHongPao authentic Teapots (RIGHT)