I just finished off a bunch of Royal Golden Yunnan that made excellent iced tea. I'm working on some Jasmine Yin Hao right now. I'm not sure what will be next up. I usually do two steepings in a 34 oz pot so I can have one warm cup and then set aside the rest in a half gallon jug to chill down.
Tough question since I drink all teas year round. However, I will say that I have more of a tendency to drink the more lightly oxidized teas during the spring and summer although I don't know why I do that. These include green, white, and the more lightly oxidized oolongs. For the green tea, I prefer Long Jing or "Dragonwell" tea. My favorite white tea is Silver Needle. Oolongs are a bit tougher because there are so many nice lightly oxidized oolongs out there. I guess I most often drink a Tie Guan Yin or a Dancong oolong. Almost forgot, I also enjoy the first flush Darjeeling teas during this time of year.
Summer is about the only time I will drink bagged teas, in the iced form. Since I usually makes 4 gallons at a time, I use strong black teas with one or two flavored herbal bags thrown in, for variety's sake. I find I especially like iced Earl Grey.