Usually, for bar use at tea houses, glass pots are for white and green teas, yixing brown ones are for oolong, and others for black and puers. The reason: not to mix up the flavors, as yixing pots are known for retaining the flavors better than other materials (legend says if you use the same yixing teapot to make the same tea 10000 times, then you can just add water (without tea leaves) and get the same tea flavor as if there were tea leaves.
If you drink tea once a day, 10000 steeps amount to 27 years 4 months and 17 days, which is doable in a lifetime. 😉
For a home (amateur) use, a porcelain teapot/gaiwan is recommended. Even better is one that is white inside because it best reflects the color of the tea, which Darius emphasizes over exact timing to ensure a good steep.