If I could, then I'd choose to live at some point in the future, probably around whichever year I could be reasonably confident that immortality in some form had been achieved. If not, then the present because of my familiarity with it, the benefits of modern technology, and the desire to see how the future turns out. If even that weren't allowed, then likely at the point where I would be the closest to the present.
If I really had to choose an entirely different civilization, though, then it's tricky. Periclean Athens and Ancient Rome during the reign of Augustus both sound tempting, and would allow me to witness some incredible history first-hand. America in the revolutionary period sounds fascinating for the same reasons (even if there's a chance I'd be drafted), and it'd have the benefits of increased familiarity with the culture and language. So in the spirit of the question, probably that.