Teapot: must be washable, large enough to hold several cups, with a spout that doesn't leak, and a comfortable handle. Jenaer glass teapots are my favorite.
Traditional teapots are ceramic, porcelain, or cast iron. If using thick-walled ceramic or cast iron teapot, rinse it with boiling water every time before putting leaves in. It will make sure the teapot will not cool your water. Rinsing doesn't hurt with porcelain or glass teapots as well. Traditional teapots often have short, leaky spouts.
Jenaer glass classic teapot ($35 for a six-cup teapot, $45 for a ten-cup teapot, ) comes very close to ideal. These teapots have hand-shaped spouts that don't leak. They are all clear glass, including replaceable infuser I actually don't use, so you can see your brew. They are dishwasher safe. They have nice elegant shape. Since they are clear and have very simple, functional design, they don't clash with anything. The only problem with glass teapots is that glass breaks. If you chip a ceramic teapot, it's chipped and ugly, but still usable. If a glass spout tip breaks off, teapot is dangerous and unusable. In my household a glass teapot lasts about six month. I have several second-best back-up ceramic teapots, which turned up in my possession one way or another. I use them mostly while my replacement Jenaer glass teapot ships.