If you use a western style ceramic teapot you can brew black tea regularly including Assam based teas, Ceylon based teas, or Kenyan based teas. Unless you start to see mold, it is best not to wash the tea pot regularly but to simply rinse it after use.
If you use a glass tea pot, it is best suited for teas with very strong flavors or very heavy tannin content such as chai tea. These glass tea pots should be cleaned thoroughly after each use. If you enjoy brewing green tea then an Eastern style ceramic tea pot is best suited because they can keep larger tea leaves back when you pour. The ceramic or clay tea pots will absorb more heat when warming the tea, compared to glass tea pots.
Overall, while there is different tea pots better suited for different teas, it is best to ensure that you only use ceramic teapots for the same tea.