Does the material of the container affect the flavor of the prepared tea? If yes, what material should be preferred to get the best results?

It shouldn't have any effect, in the sense of any flavors leaching. If your container does change the taste, you should replace it.

But it would be very unusual to chance upon a taste-changing container. Most cookware is non reactive, and containers meant for preparing and serving tea even less so. For example, untreated aluminium is reactive, but I've never heard of it being used for tea pots or tea mugs. Steel is completely OK in that regard. Melamine also has no effect on taste, but see the footnote for safety considerations.

The most likely condition under which you find a taste change would be if you are using ceramic teapots or mugs which were not mass produced for daily use, but made by a pottery hobbyist or by some exotic traditional technique which does not reach the convenience standards of modern mass production. In that case, you can simply switch the container to a neutral one, if the taste bothers you, or if you are worried about the safety of glaze leaching into your drink.

Why porcelain or glazed earthenware

No special reason. What you cite is an ISO standard. It wasn't made for people making tea at home, they wanted to have perfect reproducibility, and the easiest way is to restrict as many variables as possible. So they took one of the traditional choices and prescribed it in their standard. There is no reason to follow that standard when you make tea for drinking.

The material affects the taste of the tea in other ways: it has an influence on the speed of cooling down. But it is impossible to make a general recommendation here, as 1) there are many other factors influencing the cooling speed, and 2) people have different preferences for the taste of tea. The only relevance here is that, if you have found a process which produces tea you like with one set of utensils, it might produce a different taste if you use a different teapot, and you'll have to experiment until you have calibrated the process to your preferences again. But the differences here are subtle, you have to be a pretty dedicated tea drinker to be bothered by them.

Footnote on melamine safety: Melamine is a resin which contains traces of formaldehyde, a known carcinogen. The formaldehyde does not end up in the food at room temperature, but it starts leaching at higher temperatures, this is why it is not microwave safe. As the leaching process is gradual, and depends on pH besides temperature, there is no hard temperature prescription beyond which it is considered unsafe to use. But I couldn't find any source rating melamine for over 100 Celsius, and some of them give a lower temperature such as 60 or 70 Celsius. If you are concerned about the formaldehyde, you are probably better off choosing another mug. Porcelain is the standard choice, but steel and some plastics are also frequently used. For a short consumer info on melamine, see http://www.fda.gov/Food/ResourcesForYou/Consumers/ucm199525.htm.

Although not directly an answer to the material question, I want to point out that the shape of your cup can have a pretty big influence on the taste as well.

Most commonly known is the fact that wine is served in special glasses that support the way you can taste the wine. In this case, the shape of the glas directs a lot of the smell directly into your nose, so it is more intense.[1]

Since the perceived flavor does not only depend on tasting with the tounge, but also on the olfactory sense of the nose (a lot!), the smell of a liquid can have a direct influence on the perceived flavor.{2} (last paragraph), {3} (already in introduction, see further sources linked in paper)

So, you might find that using a large cup (so your nose is "inside" the cup while drinking and you can smell the vapor) might produce a different perceived flavor than a small cup with a very small opening.

[1] pretty obvious when comparing the smell that you perceive when drinking wine from a big red wine glass (much smell) or directly from a bottle (almost no smell since your lips block the opening of the bottle)