Your best bet for green tea, is called "Sen-Cha" it is thin and almost
looks like blades of grass in loose form. You can get sencha in tea bag
form very inexpensively from asian markets or even speacialty
tea/coffee shops.

My personal favorite is a loose form of Jasmine Green tea "pearls" they
are small little balls that unfurl in your cup and make an amazing cup
of tea.

Great easy to find green teas are the Tazo brand. "China Green Tips"
"Zen" "Lotus Root Green Tea" and I think they have a ginger green tea
too.

Many "green" teas will actually produce brown tea, but Sen-Cha will
produce a bright green cup that is unmatched. A highly prized form of
green tea called "Ma-Cha" which is a powdered green tea is considered
one of the best and is the central part of the tea ceremony.

Hope that helps! Enjoy