I really don't care that much for the Green Tea taste, but Lipton makes a green tea with lemon and ginsing which is pretty good. I still mix it half and half with an orange and black pekoe tea (regular tea) and drink it iced.
I've been drinking green tea for many years now. If you can find the loose green tea in an asian foods store, get it. You just drop a few leaves into a cup and pour hot water in it. Or make a pot of it and drink it throughout the day.
The bag type is just more convenient, but do not leave the bag in too long (no more than 3-5 min) as it will make the drink too bitter to enjoy. One of those green tea bags can probably make a few cups. Drink when you can hold side of the cup without being burning hot.