The closer to the present, the better. Modern medicine is wonderful, even with all its flaws, and the further you get from the present, the greater the risks. We're probably also living in a very peaceful time in history, relatively speaking, and not only that, most of us probably aren't getting conscripted unlike what would have happened in the past.
If I had to pick a time (and a place) in the past, a relatively peaceful period would be my primary criteria though. I don't think I'm qualified to pick anything in particular, because while I think I have reasonable knowledge of the past, it tends to focus on important events, which tend to be quite turbulent. I also lack the knowledge about everyday life in many times and cultures. Some of the times and cultures that interest me are antiquity as well as the long history of China, or perhaps even Japan, but there's probably much else that's interesting too. There might also be good times in the caliphates of Islam, for example, considering how it sounds like they were some of the more advanced cultures of the world at the time. Of course a major issue is that in most cases dating really far back, the chances are I'd probably be mostly familiar with the place I was born in and not really much else, so I'm not sure how much it would actually matter where and when I was born.
