Recommended tea ware for green tea

If it were me, I'd recommend a thin wall (eggshell) porcelain gaiwan. I'm not sure what you mean about the air, though. I don't think there should be air circulating inside the pot, gaiwan, so not sure what you mean there.

They won't ship out of the US / Canada through their cart system (you could try emailing them, though, or seeing if someone in the US can order one for you), but the one I'd really recommend is one of these three
http://www.theteagallery.com/category_s/12.htm

Very comfortable to use (you can see some topics about them on Teachat if you want some more opinions), and pretty delicate. They generally pack them very well.

As far as size, depends how you're going to drink the tea (whether you're going to pour the tea into a fair cup or drinking cup, or drink straight from the gaiwan), and how many people you'll be drinking with. I usually drink oolongs and puers, and usually use smallish cups (15-50 ml) and a lot of infusions, so I like the 60 ml one for drinking alone, and larger ones when drinking with 3 or more people. But with green tea, you tend to do fewer infusions and drink more at a time, so I'd say around 90-100 ml might not be a bad size.

Again, just depends on the size of your cups and how much tea you like to drink at once. To me, 90ml is plenty big for up to 2 or 3 people; if you've got some cups that are around 30-50 ml, you should be good (the tea will take up some volume, but possibly not as much as you think, and you aren't going to fill the cups to the rim).

If Tea Gallery won't ship, you could try http://jingteashop.com/ (based in China).

They have only a limited selection of porcelain on their site, but can generally find other stuff if you contact them directly. Overall, I think the quality of their porcelain is good.

Best Tea House also has some really nice, thin blue and white porcelain gaiwans (you can see some in the pictures I posted in the teaware thread) that are about the right size; they don't have an online shop, but I can put you in touch with folks at the HK or Canada branch if you want to try to order one. The price won't be super cheap - I'd guess around 30 US, give or take.

Again, I would recommend (and I think many others also) using porcelain rather than stoneware / earthenware for brewing green tea. There's little benefit to using a yixing pot, and the pot will make it easier to "cook" the tea; you might also lose some fragrance.

Since you mention jasmine tea specifically, I would also caution against brewing scented teas like jasmine tea in a yixing pot, for reasons that will probably be obvious if you think about it a little.

As far as brewing different types of teas in your pot, at the beginning, it may be ok to try some different teas in your pot to see what works well, but I think most people would agree it's better to devote a pot to specific types of tea, though there is some disagreement about how specific that should get.