My favorite green tea is some Sri Lankan green teas (Idulgashinna estate if I spelled that correctly).
As for if organic matters? I'd say nope. Country of origin matters more. If I was worried about if something was organic or conventional, I'd buy conventional Japanese green teas over 'organic' Chinese ones. I trust a developed countries health standards more than a developing one (that seems to have lots of food labeling problems....remember the baby milk fiasco??).
I don't know much about different Brands, but there are a ton of different Green Teas. Matcha is my favorite, for sure. Especially with a little creme and sugar added. (It's fine on its own, very grassy. I just like adding things to other things.) Sencha is also really good, a bit stronger than that matcha, I think. Genmaicha is good in the winter, it has dried brown rice in it and has a very brothy taste.
None, but I will recommend one of the best English Breakfast teas I've had in a long time: Five Roses, a South African brand. Strong and hearty w/o being bitter, and stands up well to cream, if you like it that way.