You've got it handled for Chinese green teas. Theres no better way to make them than with a gaiwan.
Japanese greens, however, enjoy different brewing vessels called kyuusu. Kyuusu simply means Japanese tea pot, but most times kyuusu are also found as side handled teapots. The most revered of these teapots are made in Tokoname, Japan. Something to think about when ordering kyuusu is what kind of sasame(filter used to keep the tea leaves in the pot) is employed. You can find steel ones, and clay ones. I believe I speak for mostly everyone when I say that the clay sasame are more preferable. They seem to be more traditional, and with a clay sasame, theres no worrying that steel is messing with the flavors of your tea. If you're looking for a really nice one, you might want to look into Tokoname ware. http://www.ArtisticNippon.com
has a good selection of really nice-looking pots. If you still want a Tokoname teapot, but would rather experiment with an entry level one, then http://www.Rishi-Tea.com
has a couple good ones.
Of course, this is all considering you want to drink Japanese greens.
May GOD bless your soul if you don't.