Tokoname is generally used for Japanese green tea, but that's not to say nothing else will brew in them. The only thing to look out for is brewing vastly different teas in unglazed teaware, which is also important for Yixing (mentioned later).
Conventional wisdom says greens and whites are too delicate to brew in Yixing-ware, but there are some who disagree. Just try it out and see what works for you.
Yixing dedication can be as specific as you want it to be-- it mostly depends on how picky your palate is and how much money you want to spend on your teawares.
For example, I have one teapot for Wuyi and other high roast, heavy feeling teas; one for Low-roast, low-oxidation oolongs like some kinds of Taiwanese gao shan and some kinds of TGY; one for cooked puerh; etc.
What is most important is making sure to not mix conflicting and/or strong flavors. You may notice that cooked puerh is the *only* thing that goes into my cooked puerh teapot because it is so strongly flavored, but that I will brew either Wuyi oolong or certain dark-roasted in the same pot because they don't clash too much. Some would say they are not similar enough, and would probably use two different pots, so it's really a matter of preference.
Anyway, hope this helps!