Original poster (me): can you tolerate any caffeine at all? Is the
equivalent of a couple of sips of Coke too much?

If so, then you should probably avoid the "first steep trick" that
some people have mentioned, and possibly also decaffeinated teas.

I would try rooibos (red bush), which is readily available nowadays,
and is rich in antioxidants, and devoid of any caffeine. It has a
sweetish taste, kind of like Thai tea (similar color, too), and it's
not very expensive. Excellent iced, too. The quality doesn't vary as
much, in my experience, as standard green and black teas--rooibos is
rooibos.

It has a number of health benefits, like green tea, if that's what
you're looking for. (just Google it and you'll see)

I personally like it, some whites, and smokier Chinese greens, but the
latter two have caffeine in them. :-(

-Jason