After thinking about it a bit, even the unglazed gaiwans have advantages. Other than personal preference (preferring a gaiwan shape over a teapot), you actually get a good deal more control with a gaiwan than a teapot. A teapot will always pour at pretty much the same rate, but a gaiwan can be opened to pour either slowly or quickly.
I really think that you ultimately want as many different types of brewing vessels as you can get. I use different types of vessels for every different type of tea. They all have advantages and disadvantages, and it's good to be able to select the right vessel for the tea you want. This is also a very good way to learn. Gaiwans are great in the beginning because of their versatility (as well as 'everyday' drinking for the same reason), and are The Right Tool for many teas. Then when you get good at using them and get an idea of what teas you like then you can start looking into yixing pots. By that time you will be more likely to have an idea of what you want to dedicate a pot to and some of the characteristics to look for (fast/slow pour, etc).
You can wash glazed yixing if you really want to, though soaking in boiling water and wiping off with a paper towel is usually sufficient.i just have the feeling that cups and gaiwans should be porcelain or something
Like I say, though, everything is going to have it's advantages or disadvantages. When it comes to tea, I don't think of anything as good or bad, right or wrong. I just ask what each tea or teaware has to offer. I generally feel that to limit what teaware I use would be to limit my knowledge of tea, and might even lead to missing out on what all a tea might offer. Results can sometimes surprise you.
