You're going to want a teapot made of glazed ceramic, porcelain or other neutral material. Unglazed clay pots, like those tokoname pots or chinese yixing pots, are generally made to brew a specific kind of tea, and won't give the best results if you mix teas or use something that doesn't match well with the clay. Unsurprisingly, Japanese pots (like those ones on artistic nippon), are best with Japanese green teas while Chinese yixing pots tend to be best with Chinese oolong and pu'er teas.
As far as size goes, that's for you to decide. It depends on 1) how many people you're usually serving and 2) how you brew your tea. Given what information you've told us, I suspect you're probably brewing a mug or cup of tea at a time for yourself or maybe a couple people. Those of us who delve more deeply into the hobby of tea, or those of us who come from an East Asian background, tend to brew much smaller amounts at once but usually compensate with repeated brewing. However I'm going to assume that you probably brew "Western style," i.e. toss a tablespoon or two of leaves into a pot, fill with boiling water, and let sit for a few minutes. If this is the case, then read on. If it's not the case, then I would suspect that you know more about tea than you're letting on.
A coffee mug is usually one cup or 8oz or about 250mL in size, so if we use that as a standard measurement, then a 250mL pot will brew one cup of tea at a time for yourself. Keep in mind that you can always use a bigger pot of tea to brew smaller amounts of tea - to a point. It's impossible to brew 80 or 100mL of tea in a one liter pot. So 250mL / 8oz is a starting point for size. I wouldn't go much below that for now, or else you'll find yourself lacking tea. Of course you can and should break this "rule" if, like deb pointed out, you tend to brew many many steepings of tea. But my hunch is that you usually don't brew more than 3 or 4 steepings of a tea before tossing the leaves. Forgive me if I'm wrong
A few other points to consider.
First, the filter. Artisan pots like those on Artistic Nippon usually come with a ceramic filter. These are great for high quality, whole leaf teas. However, dustier teas like most jasmine teas, supermarket grade loose-leaf tea, herbals, and so on need a finer filter. Usually stainless steel mesh is a good choice, though some people feel that it alters the taste of the tea. Frankly, I don't think it's a big deal most of the time. You can find pots that have a stainless steel filter at the spout, which is nice because the leaves can expand in the body of the pot, or you can find teapots that use a basket filter, which is ten times easier to clean up, plus you can simply lift the basket out of the pot to prevent overbrewing if you're not going to drink the whole pot all at once.
Second, if you just want a pretty pot, there are many places to find that, and you shouldn't worry so much about what we're saying. If you're looking for something that's more on the practical side, then there are many other, much cheaper brewing tools than a teapot that will serve you better. If you're looking for a mix of form and function that a teapot provides, then the advice in this thread so far is worth heeding.
Third, in terms of cups - get some cups that you like to look at, will hold the right amount of tea, and that don't get too hot when you hold them. Some tips - thick ceramics and cast iron get really hot. Too-big handleless cups are nice because, if filled only halfway, the rim generally doesn't get too hot to hold. Most important is that you like them. The more you like them, the more you'll use them. Again, stick to porcelain, glass, glazed stoneware - something neutral.
Hope this helps,
hope you enjoy many cups of tea.
(let us know if you just want links to places that sell the kind of teapot you want - we're happy to oblige