The servers with 3 chocobos according to a recent thread on the official forums...
I dunno which is best for other peak hours besides JP or if one of the 2 chocobo servers would be better. I have another character on Gysahl and Selbina seems to have more action goin' on at all times of the day in comparison.
A chocobo beside the server listing only indicates how many people are currently online, not the actual server population.
I guess it depends on what you'd like to do. Selbina & Mysidia are both very good servers with decent populations, though everyone still hovers around Ul'Dah. Besaid I hear is kind of an unofficial RP server if you're into that sort of thing. Personally I wouldn't worry too much about which server has populations at this point, since at PS3 launch there will be an influx of players anyway.
Try posting on the forums (Lodestone, ZAM, BG, Pro, etc.) and try to find yourself a nice, active social LS to get you started and everything will work out.