Not cleaning is a bit weird - especially if you intend to use different types of tea; also if your water is hard, they get gunky if you don't change the water filter soon enough.
Largely to keep it clean, I prefer teapots with short spouts - inspired by the stump teapot that someone linked to above, although I've always thought they're expensive & not had a real one, but similar shapes.
I also like white china teapots, again, so I can see it's clean, and I prefer ones that are slightly larger than you need - when you tip it forward, less likely to dribble from the lid; for two mugs - typically 500ml of tea, I prefer a teapot with a capacity of 600-700ml.
Current favourites are one from George at Asda (cheap £6 emergency purchase when I rented a cottage with no teapot provided), White Teapot | Home | George at ASDA
And one that turned out to be mainly for the catering market from TK Maxx - super easy to clean.
A good tea cosy is a must - nothing nicer that going to pour it and the handle has warmed up a teensy bit too hot to hold - cotton with a foam lining my favourite.