Hey Matt! There are names for certain specific names for shapes, but generally speaking most people just refer to the pots by the name of the shape. So I would just call that that an unglazed rectangle-a very simple unglazed rectangle. Many pot shapes are modeled after the first containers made in China hundreds of years ago. I have an antique Chinese pot (Nakawatari) in that exact shape. Often new quality pots make in Japan are still modeled after antique Chinese containers, but there are tons of variations as well.
Selecting a pot really comes down to personal preference, it's very subjective. I would recommend purchasing from Matt Owinga, through his ebay store, contacting him directly or through the facebook bonsai auction group. Michael Ryan Bell has some for sale as well, or you can just scan through Ebay to check some out. A great "Bang for your buck" type of pot in classical shapes are made in the Tokoname Regiona of Japan. Maybe try typing Tokoname into an ebay search, these are good quality pots made in Japan. Modern Chinese are lower quality than Tokoname, but some are close and very inexpensive if you find the right person to buy from. Antique Chinese and from certain Japanese makers like Gyouzan are much more expensive but great quality and may have nice patina and age to them.
If you want to learn more about ceramic containers, this is prob the best resource online.
https://japanesebonsaipots.net/
