To start off, white tea has very little caffiene compared to black and green varieties, so if you're watching you're intake it's probably a good one to drink.
I drink a lot of different teas (
www.teavana.com - has a lot of teas and info) I drink coffee in the morning and tea during the day and into the evening. I don't drink it solely for the health benefits, but it's just an added plus. I also drank it throughout my pregnancy with no problems. Most teas are fine to drink in moderation but some herbal varieties can have side effects so I would read up on any that you drink on a regular basis (e.g. chammomile can cause uterine mild uterine contractions and bleeding, so not recommended in the 1st trimester).
As for the antioxidant question, here is a Q&A from 3FC main site; the main point, you get higher levels of antioxidants if you drink the real stuff, not the decaf.
Q: Is there any difference in the antioxidant levels of regular and decaf coffees and teas? Also, despite the antioxidant benefits, isn’t the caffeine still bad for you?
A: Compared to decaf, regular green tea contains about three times as much EGCG, the antioxidant phytochemical that has shown cancer-prevention effects in some laboratory studies. Similarly, decaf black tea, which contains another, less-studied antioxidant called theorubigin, also has lower amounts (about 50 percent less) than its regular counterpart. Limited research suggests that chlorogenic acid, one of the main antioxidants in coffee, may be lower in decaf coffee as well. However, even with decaf versions, the true antioxidant benefits you receive depends on how much you drink. As for concerns about caffeine, when consumed in moderation, it may not be as bad as you think. Some studies now suggest that caffeine's purported role in increasing blood pressure may not be linked as strongly to coffee and tea. Note that people with sleep difficulties, however, do need to be careful about the amount and timing of caffeine consumption. Also, most health experts suggest that pregnant women limit total daily caffeine from coffee, soft drinks and other sources to about 300 milligrams, the equivalent of three 6-ounce cups of regular coffee.